---
_id: '63620'
abstract:
- lang: eng
text: We introduce a new class of reflection groups associated with the canonical
bilinear lattices of Lenzing, which we call reflection groups of canonical type.
The main result of this work is a categorification of the corresponding poset
of non-crossing partitions for any such group, realized via the poset of thick
subcategories of the category of coherent sheaves on an exceptional hereditary
curve generated by an exceptional sequence. A second principal result, essential
for the categorification, is a proof of the transitivity of the Hurwitz action
in these reflection groups.
author:
- first_name: Barbara
full_name: Baumeister, Barbara
last_name: Baumeister
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: Georges
full_name: Neaime, Georges
last_name: Neaime
- first_name: Charly Merlin
full_name: Schwabe, Charly Merlin
id: '103440'
last_name: Schwabe
citation:
ama: Baumeister B, Burban I, Neaime G, Schwabe CM. Non-crossing partitions for exceptional
hereditary curves. arXiv:251201729. Published online 2025.
apa: Baumeister, B., Burban, I., Neaime, G., & Schwabe, C. M. (2025). Non-crossing
partitions for exceptional hereditary curves. In arXiv:2512.01729.
bibtex: '@article{Baumeister_Burban_Neaime_Schwabe_2025, title={Non-crossing partitions
for exceptional hereditary curves}, journal={arXiv:2512.01729}, author={Baumeister,
Barbara and Burban, Igor and Neaime, Georges and Schwabe, Charly Merlin}, year={2025}
}'
chicago: Baumeister, Barbara, Igor Burban, Georges Neaime, and Charly Merlin Schwabe.
“Non-Crossing Partitions for Exceptional Hereditary Curves.” ArXiv:2512.01729,
2025.
ieee: B. Baumeister, I. Burban, G. Neaime, and C. M. Schwabe, “Non-crossing partitions
for exceptional hereditary curves,” arXiv:2512.01729. 2025.
mla: Baumeister, Barbara, et al. “Non-Crossing Partitions for Exceptional Hereditary
Curves.” ArXiv:2512.01729, 2025.
short: B. Baumeister, I. Burban, G. Neaime, C.M. Schwabe, ArXiv:2512.01729 (2025).
date_created: 2026-01-15T09:37:34Z
date_updated: 2026-01-16T09:09:17Z
external_id:
arxiv:
- '2512.01729'
language:
- iso: eng
publication: arXiv:2512.01729
status: public
title: Non-crossing partitions for exceptional hereditary curves
type: preprint
user_id: '103440'
year: '2025'
...
---
_id: '44328'
abstract:
- lang: eng
text: In this paper, we study equivalences between the categories of quasi–coherent
sheaves on non–commutative noetherian schemes. In particular, we give a new proof
of Căldăraru's conjecture about Morita equivalences of Azumaya algebras on noetherian
schemes. Moreover, we derive necessary and sufficient condition for two reduced
non–commutative curves to be Morita equivalent.
article_number: '108273'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: Yu.
full_name: Drozd, Yu.
last_name: Drozd
citation:
ama: Burban I, Drozd Yu. Morita theory for non-commutative noetherian schemes. Advances
in Mathematics. 2022;399. doi:10.1016/j.aim.2022.108273
apa: Burban, I., & Drozd, Yu. (2022). Morita theory for non-commutative noetherian
schemes. Advances in Mathematics, 399, Article 108273. https://doi.org/10.1016/j.aim.2022.108273
bibtex: '@article{Burban_Drozd_2022, title={Morita theory for non-commutative noetherian
schemes}, volume={399}, DOI={10.1016/j.aim.2022.108273},
number={108273}, journal={Advances in Mathematics}, author={Burban, Igor and Drozd,
Yu.}, year={2022} }'
chicago: Burban, Igor, and Yu. Drozd. “Morita Theory for Non-Commutative Noetherian
Schemes.” Advances in Mathematics 399 (2022). https://doi.org/10.1016/j.aim.2022.108273.
ieee: 'I. Burban and Yu. Drozd, “Morita theory for non-commutative noetherian schemes,”
Advances in Mathematics, vol. 399, Art. no. 108273, 2022, doi: 10.1016/j.aim.2022.108273.'
mla: Burban, Igor, and Yu. Drozd. “Morita Theory for Non-Commutative Noetherian
Schemes.” Advances in Mathematics, vol. 399, 108273, 2022, doi:10.1016/j.aim.2022.108273.
short: I. Burban, Yu. Drozd, Advances in Mathematics 399 (2022).
date_created: 2023-05-02T18:34:25Z
date_updated: 2023-05-07T01:35:27Z
department:
- _id: '602'
doi: 10.1016/j.aim.2022.108273
intvolume: ' 399'
language:
- iso: eng
publication: Advances in Mathematics
publication_status: published
status: public
title: Morita theory for non-commutative noetherian schemes
type: journal_article
user_id: '49063'
volume: 399
year: '2022'
...
---
_id: '44537'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: C.
full_name: Alfes-Neumann, C.
last_name: Alfes-Neumann
- first_name: M.
full_name: Raum, M.
last_name: Raum
citation:
ama: Burban I, Alfes-Neumann C, Raum M. A classification of polyharmonic Maa forms
via quiver representations. Published online 2022.
apa: Burban, I., Alfes-Neumann, C., & Raum, M. (2022). A classification of
polyharmonic Maa forms via quiver representations.
bibtex: '@article{Burban_Alfes-Neumann_Raum_2022, title={A classification of polyharmonic
Maa forms via quiver representations}, author={Burban, Igor and Alfes-Neumann,
C. and Raum, M.}, year={2022} }'
chicago: Burban, Igor, C. Alfes-Neumann, and M. Raum. “A Classification of Polyharmonic
Maa Forms via Quiver Representations,” 2022.
ieee: I. Burban, C. Alfes-Neumann, and M. Raum, “A classification of polyharmonic
Maa forms via quiver representations.” 2022.
mla: Burban, Igor, et al. A Classification of Polyharmonic Maa Forms via Quiver
Representations. 2022.
short: I. Burban, C. Alfes-Neumann, M. Raum, (2022).
date_created: 2023-05-07T00:54:50Z
date_updated: 2023-05-07T01:37:00Z
department:
- _id: '602'
language:
- iso: eng
main_file_link:
- url: https://doi.org/10.48550/arXiv.2207.02278
publication_status: published
status: public
title: A classification of polyharmonic Maa forms via quiver representations
type: preprint
user_id: '49063'
year: '2022'
...
---
_id: '44327'
article_number: '104499'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: A.
full_name: Peruzzi, A.
last_name: Peruzzi
citation:
ama: Burban I, Peruzzi A. On elliptic solutions of the associative Yang-Baxter equation.
Journal of Geometry and Physics. 2022;176.
apa: Burban, I., & Peruzzi, A. (2022). On elliptic solutions of the associative
Yang-Baxter equation. Journal of Geometry and Physics, 176, Article
104499.
bibtex: '@article{Burban_Peruzzi_2022, title={On elliptic solutions of the associative
Yang-Baxter equation}, volume={176}, number={104499}, journal={Journal of Geometry
and Physics}, author={Burban, Igor and Peruzzi, A.}, year={2022} }'
chicago: Burban, Igor, and A. Peruzzi. “On Elliptic Solutions of the Associative
Yang-Baxter Equation.” Journal of Geometry and Physics 176 (2022).
ieee: I. Burban and A. Peruzzi, “On elliptic solutions of the associative Yang-Baxter
equation,” Journal of Geometry and Physics, vol. 176, Art. no. 104499,
2022.
mla: Burban, Igor, and A. Peruzzi. “On Elliptic Solutions of the Associative Yang-Baxter
Equation.” Journal of Geometry and Physics, vol. 176, 104499, 2022.
short: I. Burban, A. Peruzzi, Journal of Geometry and Physics 176 (2022).
date_created: 2023-05-02T18:32:49Z
date_updated: 2023-05-07T01:41:35Z
department:
- _id: '602'
intvolume: ' 176'
language:
- iso: eng
publication: Journal of Geometry and Physics
publication_status: published
status: public
title: On elliptic solutions of the associative Yang-Baxter equation
type: journal_article
user_id: '49063'
volume: 176
year: '2022'
...
---
_id: '44329'
abstract:
- lang: eng
text: This paper is devoted to algebro-geometric study of infinite dimensional Lie
bialgebras, which arise from solutions of the classical Yang–Baxter equation.
We regard trigonometric solutions of this equation as twists of the standard Lie
bialgebra cobracket on an appropriate affine Lie algebra and work out the corresponding
theory of Manin triples, putting it into an algebro-geometric context. As a consequence
of this approach, we prove that any trigonometric solution of the classical Yang–Baxter
equation arises from an appropriate algebro-geometric datum. The developed theory
is illustrated by some concrete examples.
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: R.
full_name: Abedin, R.
last_name: Abedin
citation:
ama: Burban I, Abedin R. Algebraic geometry of Lie bialgebras defined by solutions
of the classical Yang-Baxter equation. Communications in Mathematical Physics.
2021;387(2):1051–1109. doi:10.1007/s00220-021-04188-7
apa: Burban, I., & Abedin, R. (2021). Algebraic geometry of Lie bialgebras defined
by solutions of the classical Yang-Baxter equation. Communications in Mathematical
Physics, 387(2), 1051–1109. https://doi.org/10.1007/s00220-021-04188-7
bibtex: '@article{Burban_Abedin_2021, title={Algebraic geometry of Lie bialgebras
defined by solutions of the classical Yang-Baxter equation}, volume={387}, DOI={10.1007/s00220-021-04188-7},
number={2}, journal={Communications in Mathematical Physics}, author={Burban,
Igor and Abedin, R.}, year={2021}, pages={1051–1109} }'
chicago: 'Burban, Igor, and R. Abedin. “Algebraic Geometry of Lie Bialgebras Defined
by Solutions of the Classical Yang-Baxter Equation.” Communications in Mathematical
Physics 387, no. 2 (2021): 1051–1109. https://doi.org/10.1007/s00220-021-04188-7.'
ieee: 'I. Burban and R. Abedin, “Algebraic geometry of Lie bialgebras defined by
solutions of the classical Yang-Baxter equation,” Communications in Mathematical
Physics, vol. 387, no. 2, pp. 1051–1109, 2021, doi: 10.1007/s00220-021-04188-7.'
mla: Burban, Igor, and R. Abedin. “Algebraic Geometry of Lie Bialgebras Defined
by Solutions of the Classical Yang-Baxter Equation.” Communications in Mathematical
Physics, vol. 387, no. 2, 2021, pp. 1051–1109, doi:10.1007/s00220-021-04188-7.
short: I. Burban, R. Abedin, Communications in Mathematical Physics 387 (2021) 1051–1109.
date_created: 2023-05-02T18:36:54Z
date_updated: 2023-05-07T01:35:11Z
department:
- _id: '602'
doi: 10.1007/s00220-021-04188-7
intvolume: ' 387'
issue: '2'
language:
- iso: eng
page: 1051–1109
publication: Communications in Mathematical Physics
publication_status: published
status: public
title: Algebraic geometry of Lie bialgebras defined by solutions of the classical
Yang-Baxter equation
type: journal_article
user_id: '49063'
volume: 387
year: '2021'
...
---
_id: '44331'
abstract:
- lang: eng
text: In this paper, we study properties of the algebras of planar quasi-invariants.
These algebras are Cohen–Macaulay and Gorenstein in codimension one. Using the
technique of matrix problems, we classify all Cohen–Macaulay modules of rank one
over them and determine their Picard groups. In terms of this classification,
we describe the spectral modules of the planar rational Calogero–Moser systems.
Finally, we elaborate the theory of the algebraic inverse scattering method, providing
explicit computations of some ‘isospectral deformations’ of the planar rational
Calogero–Moser system in the case of the split rational potential.
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: A.
full_name: Zheglov, A.
last_name: Zheglov
citation:
ama: Burban I, Zheglov A. Cohen-Macaulay modules over the algebra of planar quasi-invariants
and Calogero-Moser systems. Proceedings of the London Mathematical Society.
2020;121(4):1033–1082. doi:10.1112/plms.12341
apa: Burban, I., & Zheglov, A. (2020). Cohen-Macaulay modules over the algebra
of planar quasi-invariants and Calogero-Moser systems. Proceedings of the London
Mathematical Society, 121(4), 1033–1082. https://doi.org/10.1112/plms.12341
bibtex: '@article{Burban_Zheglov_2020, title={Cohen-Macaulay modules over the algebra
of planar quasi-invariants and Calogero-Moser systems}, volume={121}, DOI={10.1112/plms.12341}, number={4},
journal={Proceedings of the London Mathematical Society}, author={Burban, Igor
and Zheglov, A.}, year={2020}, pages={1033–1082} }'
chicago: 'Burban, Igor, and A. Zheglov. “Cohen-Macaulay Modules over the Algebra
of Planar Quasi-Invariants and Calogero-Moser Systems.” Proceedings of the
London Mathematical Society 121, no. 4 (2020): 1033–1082. https://doi.org/10.1112/plms.12341.'
ieee: 'I. Burban and A. Zheglov, “Cohen-Macaulay modules over the algebra of planar
quasi-invariants and Calogero-Moser systems,” Proceedings of the London Mathematical
Society, vol. 121, no. 4, pp. 1033–1082, 2020, doi: 10.1112/plms.12341.'
mla: Burban, Igor, and A. Zheglov. “Cohen-Macaulay Modules over the Algebra of Planar
Quasi-Invariants and Calogero-Moser Systems.” Proceedings of the London Mathematical
Society, vol. 121, no. 4, 2020, pp. 1033–1082, doi:10.1112/plms.12341.
short: I. Burban, A. Zheglov, Proceedings of the London Mathematical Society 121
(2020) 1033–1082.
date_created: 2023-05-02T18:47:19Z
date_updated: 2023-05-07T01:30:54Z
department:
- _id: '602'
doi: 10.1112/plms.12341
intvolume: ' 121'
issue: '4'
language:
- iso: eng
page: 1033–1082
publication: Proceedings of the London Mathematical Society
publication_status: published
status: public
title: Cohen-Macaulay modules over the algebra of planar quasi-invariants and Calogero-Moser
systems
type: journal_article
user_id: '49063'
volume: 121
year: '2020'
...
---
_id: '44333'
abstract:
- lang: eng
text: This work deals with an algebro–geometric theory of solutions of the classical
Yang–Baxter equation based on torsion free coherent sheaves of Lie algebras on
Weierstraß cubic curves.
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: L.
full_name: Galinat, L.
last_name: Galinat
citation:
ama: Burban I, Galinat L. Torsion free sheaves on Weierstraß cubic curves and the
classical Yang-Baxter equation. Communications in Mathematical Physics.
2018;364(1):123–169. doi:10.1007/s00220-018-3172-2
apa: Burban, I., & Galinat, L. (2018). Torsion free sheaves on Weierstraß cubic
curves and the classical Yang-Baxter equation. Communications in Mathematical
Physics, 364(1), 123–169. https://doi.org/10.1007/s00220-018-3172-2
bibtex: '@article{Burban_Galinat_2018, title={Torsion free sheaves on Weierstraß
cubic curves and the classical Yang-Baxter equation}, volume={364}, DOI={10.1007/s00220-018-3172-2},
number={1}, journal={Communications in Mathematical Physics}, author={Burban,
Igor and Galinat, L.}, year={2018}, pages={123–169} }'
chicago: 'Burban, Igor, and L. Galinat. “Torsion Free Sheaves on Weierstraß Cubic
Curves and the Classical Yang-Baxter Equation.” Communications in Mathematical
Physics 364, no. 1 (2018): 123–169. https://doi.org/10.1007/s00220-018-3172-2.'
ieee: 'I. Burban and L. Galinat, “Torsion free sheaves on Weierstraß cubic curves
and the classical Yang-Baxter equation,” Communications in Mathematical Physics,
vol. 364, no. 1, pp. 123–169, 2018, doi: 10.1007/s00220-018-3172-2.'
mla: Burban, Igor, and L. Galinat. “Torsion Free Sheaves on Weierstraß Cubic Curves
and the Classical Yang-Baxter Equation.” Communications in Mathematical Physics,
vol. 364, no. 1, 2018, pp. 123–169, doi:10.1007/s00220-018-3172-2.
short: I. Burban, L. Galinat, Communications in Mathematical Physics 364 (2018)
123–169.
date_created: 2023-05-02T18:50:35Z
date_updated: 2023-05-07T01:34:43Z
department:
- _id: '602'
doi: 10.1007/s00220-018-3172-2
intvolume: ' 364'
issue: '1'
language:
- iso: eng
page: 123–169
publication: Communications in Mathematical Physics
publication_status: published
status: public
title: Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter
equation
type: journal_article
user_id: '49063'
volume: 364
year: '2018'
...
---
_id: '44538'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: Yu.
full_name: Drozd, Yu.
last_name: Drozd
citation:
ama: Burban I, Drozd Yu. Non-commutative nodal curves and derived tame algebras.
Published online 2018.
apa: Burban, I., & Drozd, Yu. (2018). Non-commutative nodal curves and derived
tame algebras.
bibtex: '@article{Burban_Drozd_2018, title={Non-commutative nodal curves and derived
tame algebras}, author={Burban, Igor and Drozd, Yu.}, year={2018} }'
chicago: Burban, Igor, and Yu. Drozd. “Non-Commutative Nodal Curves and Derived
Tame Algebras,” 2018.
ieee: I. Burban and Yu. Drozd, “Non-commutative nodal curves and derived tame algebras.”
2018.
mla: Burban, Igor, and Yu. Drozd. Non-Commutative Nodal Curves and Derived Tame
Algebras. 2018.
short: I. Burban, Yu. Drozd, (2018).
date_created: 2023-05-07T00:56:31Z
date_updated: 2023-05-07T01:36:42Z
department:
- _id: '602'
language:
- iso: eng
main_file_link:
- url: https://doi.org/10.48550/arXiv.1805.05174
publication_status: published
status: public
title: Non-commutative nodal curves and derived tame algebras
type: preprint
user_id: '49063'
year: '2018'
...
---
_id: '44332'
article_number: 1850064-46 pp
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: A.
full_name: Zheglov, A.
last_name: Zheglov
citation:
ama: Burban I, Zheglov A. Fourier-Mukai transform on Weierstraß cubics and commuting
differential operators. International Journal of Mathematics. 2018;29(10).
apa: Burban, I., & Zheglov, A. (2018). Fourier-Mukai transform on Weierstraß
cubics and commuting differential operators. International Journal of Mathematics,
29(10), Article 1850064- 46 pp.
bibtex: '@article{Burban_Zheglov_2018, title={Fourier-Mukai transform on Weierstraß
cubics and commuting differential operators}, volume={29}, number={101850064–46
pp}, journal={International Journal of Mathematics}, author={Burban, Igor and
Zheglov, A.}, year={2018} }'
chicago: Burban, Igor, and A. Zheglov. “Fourier-Mukai Transform on Weierstraß Cubics
and Commuting Differential Operators.” International Journal of Mathematics
29, no. 10 (2018).
ieee: I. Burban and A. Zheglov, “Fourier-Mukai transform on Weierstraß cubics and
commuting differential operators,” International Journal of Mathematics,
vol. 29, no. 10, Art. no. 1850064–46 pp, 2018.
mla: Burban, Igor, and A. Zheglov. “Fourier-Mukai Transform on Weierstraß Cubics
and Commuting Differential Operators.” International Journal of Mathematics,
vol. 29, no. 10, 1850064-46 pp, 2018.
short: I. Burban, A. Zheglov, International Journal of Mathematics 29 (2018).
date_created: 2023-05-02T18:49:12Z
date_updated: 2023-05-07T01:41:27Z
department:
- _id: '602'
intvolume: ' 29'
issue: '10'
language:
- iso: eng
publication: International Journal of Mathematics
publication_status: published
status: public
title: Fourier-Mukai transform on Weierstraß cubics and commuting differential operators
type: journal_article
user_id: '49063'
volume: 29
year: '2018'
...
---
_id: '44337'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: Yu.
full_name: Drozd, Yu.
last_name: Drozd
citation:
ama: Burban I, Drozd Yu. Maximal Cohen-Macaulay Modules over Non-Isolated Surface
Singularities and Matrix Problems. Vol 248. 1178th ed.; 2017. doi:10.1090/memo/1178
apa: Burban, I., & Drozd, Yu. (2017). Maximal Cohen-Macaulay modules over
non-isolated surface singularities and matrix problems (1178th ed., Vol. 248).
https://doi.org/10.1090/memo/1178
bibtex: '@book{Burban_Drozd_2017, edition={1178}, series={Memoirs of the American
Mathematical Society}, title={Maximal Cohen-Macaulay modules over non-isolated
surface singularities and matrix problems}, volume={248}, DOI={10.1090/memo/1178},
author={Burban, Igor and Drozd, Yu.}, year={2017}, collection={Memoirs of the
American Mathematical Society} }'
chicago: Burban, Igor, and Yu. Drozd. Maximal Cohen-Macaulay Modules over Non-Isolated
Surface Singularities and Matrix Problems. 1178th ed. Vol. 248. Memoirs of
the American Mathematical Society, 2017. https://doi.org/10.1090/memo/1178.
ieee: I. Burban and Yu. Drozd, Maximal Cohen-Macaulay modules over non-isolated
surface singularities and matrix problems, 1178th ed., vol. 248. 2017.
mla: Burban, Igor, and Yu. Drozd. Maximal Cohen-Macaulay Modules over Non-Isolated
Surface Singularities and Matrix Problems. 1178th ed., vol. 248, 2017, doi:10.1090/memo/1178.
short: I. Burban, Yu. Drozd, Maximal Cohen-Macaulay Modules over Non-Isolated Surface
Singularities and Matrix Problems, 1178th ed., 2017.
date_created: 2023-05-02T18:59:05Z
date_updated: 2023-05-07T01:33:37Z
department:
- _id: '602'
doi: 10.1090/memo/1178
edition: '1178'
extern: '1'
intvolume: ' 248'
language:
- iso: eng
publication_identifier:
isbn:
- 978-1-4704-2537-1
publication_status: published
series_title: Memoirs of the American Mathematical Society
status: public
title: Maximal Cohen-Macaulay modules over non-isolated surface singularities and
matrix problems
type: book
user_id: '49063'
volume: 248
year: '2017'
...
---
_id: '44539'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: Yu.
full_name: Drozd, Yu.
last_name: Drozd
citation:
ama: 'Burban I, Drozd Yu. On the derived categories of gentle and skew-gentle algebras:
homological algebra and matrix problems. Published online 2017.'
apa: 'Burban, I., & Drozd, Yu. (2017). On the derived categories of gentle
and skew-gentle algebras: homological algebra and matrix problems.'
bibtex: '@article{Burban_Drozd_2017, title={On the derived categories of gentle
and skew-gentle algebras: homological algebra and matrix problems}, author={Burban,
Igor and Drozd, Yu.}, year={2017} }'
chicago: 'Burban, Igor, and Yu. Drozd. “On the Derived Categories of Gentle and
Skew-Gentle Algebras: Homological Algebra and Matrix Problems,” 2017.'
ieee: 'I. Burban and Yu. Drozd, “On the derived categories of gentle and skew-gentle
algebras: homological algebra and matrix problems.” 2017.'
mla: 'Burban, Igor, and Yu. Drozd. On the Derived Categories of Gentle and Skew-Gentle
Algebras: Homological Algebra and Matrix Problems. 2017.'
short: I. Burban, Yu. Drozd, (2017).
date_created: 2023-05-07T00:57:34Z
date_updated: 2023-05-07T01:36:54Z
department:
- _id: '602'
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://doi.org/10.48550/arXiv.1706.08358
publication_status: published
status: public
title: 'On the derived categories of gentle and skew-gentle algebras: homological
algebra and matrix problems'
type: preprint
user_id: '49063'
year: '2017'
...
---
_id: '44334'
article_number: '454002'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: L.
full_name: Galinat, L.
last_name: Galinat
citation:
ama: 'Burban I, Galinat L. Simple vector bundles on a nodal Weierstraß cubic and
quasi-trigonometric solutions of CYBE. Journal of Physics A: Mathematical and
Theoretical. 2017;50.'
apa: 'Burban, I., & Galinat, L. (2017). Simple vector bundles on a nodal Weierstraß
cubic and quasi-trigonometric solutions of CYBE. Journal of Physics A: Mathematical
and Theoretical, 50, Article 454002.'
bibtex: '@article{Burban_Galinat_2017, title={Simple vector bundles on a nodal Weierstraß
cubic and quasi-trigonometric solutions of CYBE}, volume={50}, number={454002},
journal={Journal of Physics A: Mathematical and Theoretical}, author={Burban,
Igor and Galinat, L.}, year={2017} }'
chicago: 'Burban, Igor, and L. Galinat. “Simple Vector Bundles on a Nodal Weierstraß
Cubic and Quasi-Trigonometric Solutions of CYBE.” Journal of Physics A: Mathematical
and Theoretical 50 (2017).'
ieee: 'I. Burban and L. Galinat, “Simple vector bundles on a nodal Weierstraß cubic
and quasi-trigonometric solutions of CYBE,” Journal of Physics A: Mathematical
and Theoretical, vol. 50, Art. no. 454002, 2017.'
mla: 'Burban, Igor, and L. Galinat. “Simple Vector Bundles on a Nodal Weierstraß
Cubic and Quasi-Trigonometric Solutions of CYBE.” Journal of Physics A: Mathematical
and Theoretical, vol. 50, 454002, 2017.'
short: 'I. Burban, L. Galinat, Journal of Physics A: Mathematical and Theoretical
50 (2017).'
date_created: 2023-05-02T18:51:44Z
date_updated: 2023-05-07T01:40:53Z
department:
- _id: '602'
extern: '1'
intvolume: ' 50'
language:
- iso: eng
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_status: published
status: public
title: Simple vector bundles on a nodal Weierstraß cubic and quasi-trigonometric solutions
of CYBE
type: journal_article
user_id: '49063'
volume: 50
year: '2017'
...
---
_id: '44335'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: Yu.
full_name: Drozd, Yu.
last_name: Drozd
- first_name: V.
full_name: Gavran, V.
last_name: Gavran
citation:
ama: Burban I, Drozd Yu, Gavran V. Minors of non-commutative schemes. European
Journal of Mathematics. 2017;3(2):311–341.
apa: Burban, I., Drozd, Yu., & Gavran, V. (2017). Minors of non-commutative
schemes. European Journal of Mathematics, 3(2), 311–341.
bibtex: '@article{Burban_Drozd_Gavran_2017, title={Minors of non-commutative schemes},
volume={3}, number={2}, journal={European Journal of Mathematics}, author={Burban,
Igor and Drozd, Yu. and Gavran, V.}, year={2017}, pages={311–341} }'
chicago: 'Burban, Igor, Yu. Drozd, and V. Gavran. “Minors of Non-Commutative Schemes.”
European Journal of Mathematics 3, no. 2 (2017): 311–341.'
ieee: I. Burban, Yu. Drozd, and V. Gavran, “Minors of non-commutative schemes,”
European Journal of Mathematics, vol. 3, no. 2, pp. 311–341, 2017.
mla: Burban, Igor, et al. “Minors of Non-Commutative Schemes.” European Journal
of Mathematics, vol. 3, no. 2, 2017, pp. 311–341.
short: I. Burban, Yu. Drozd, V. Gavran, European Journal of Mathematics 3 (2017)
311–341.
date_created: 2023-05-02T18:53:20Z
date_updated: 2023-05-07T01:41:05Z
department:
- _id: '602'
extern: '1'
intvolume: ' 3'
issue: '2'
language:
- iso: eng
page: 311–341
publication: European Journal of Mathematics
publication_status: published
status: public
title: Minors of non-commutative schemes
type: journal_article
user_id: '49063'
volume: 3
year: '2017'
...
---
_id: '44336'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: Yu.
full_name: Drozd, Yu.
last_name: Drozd
- first_name: V.
full_name: Gavran, V.
last_name: Gavran
citation:
ama: Burban I, Drozd Yu, Gavran V. Singular curves and quasi–hereditary algebras.
International Mathematics Research Notices 2017. 2017;(3):895-920.
apa: Burban, I., Drozd, Yu., & Gavran, V. (2017). Singular curves and quasi–hereditary
algebras. International Mathematics Research Notices 2017, 3, 895–920.
bibtex: '@article{Burban_Drozd_Gavran_2017, title={Singular curves and quasi–hereditary
algebras}, number={3}, journal={International Mathematics Research Notices 2017},
author={Burban, Igor and Drozd, Yu. and Gavran, V.}, year={2017}, pages={895–920}
}'
chicago: 'Burban, Igor, Yu. Drozd, and V. Gavran. “Singular Curves and Quasi–Hereditary
Algebras.” International Mathematics Research Notices 2017, no. 3 (2017):
895–920.'
ieee: I. Burban, Yu. Drozd, and V. Gavran, “Singular curves and quasi–hereditary
algebras,” International Mathematics Research Notices 2017, no. 3, pp.
895–920, 2017.
mla: Burban, Igor, et al. “Singular Curves and Quasi–Hereditary Algebras.” International
Mathematics Research Notices 2017, no. 3, 2017, pp. 895–920.
short: I. Burban, Yu. Drozd, V. Gavran, International Mathematics Research Notices
2017 (2017) 895–920.
date_created: 2023-05-02T18:57:28Z
date_updated: 2023-05-07T01:41:14Z
department:
- _id: '602'
extern: '1'
issue: '3'
language:
- iso: eng
page: 895-920
publication: International Mathematics Research Notices 2017
publication_status: published
status: public
title: Singular curves and quasi–hereditary algebras
type: journal_article
user_id: '49063'
year: '2017'
...
---
_id: '44339'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: W.
full_name: Gnedin, W.
last_name: Gnedin
citation:
ama: Burban I, Gnedin W. Cohen-Macaulay modules over some non-reduced curve singularities.
Journal of Pure and Applied Algebra. 2016;220(12):3777–3815.
apa: Burban, I., & Gnedin, W. (2016). Cohen-Macaulay modules over some non-reduced
curve singularities. Journal of Pure and Applied Algebra, 220(12),
3777–3815.
bibtex: '@article{Burban_Gnedin_2016, title={Cohen-Macaulay modules over some non-reduced
curve singularities}, volume={220}, number={12}, journal={Journal of Pure and
Applied Algebra}, author={Burban, Igor and Gnedin, W.}, year={2016}, pages={3777–3815}
}'
chicago: 'Burban, Igor, and W. Gnedin. “Cohen-Macaulay Modules over Some Non-Reduced
Curve Singularities.” Journal of Pure and Applied Algebra 220, no. 12 (2016):
3777–3815.'
ieee: I. Burban and W. Gnedin, “Cohen-Macaulay modules over some non-reduced curve
singularities,” Journal of Pure and Applied Algebra, vol. 220, no. 12,
pp. 3777–3815, 2016.
mla: Burban, Igor, and W. Gnedin. “Cohen-Macaulay Modules over Some Non-Reduced
Curve Singularities.” Journal of Pure and Applied Algebra, vol. 220, no.
12, 2016, pp. 3777–3815.
short: I. Burban, W. Gnedin, Journal of Pure and Applied Algebra 220 (2016) 3777–3815.
date_created: 2023-05-02T19:00:43Z
date_updated: 2023-05-07T01:41:53Z
department:
- _id: '602'
extern: '1'
intvolume: ' 220'
issue: '12'
language:
- iso: eng
page: 3777–3815
publication: Journal of Pure and Applied Algebra
publication_status: published
status: public
title: Cohen-Macaulay modules over some non-reduced curve singularities
type: journal_article
user_id: '49063'
volume: 220
year: '2016'
...
---
_id: '44340'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: T.
full_name: Henrich, T.
last_name: Henrich
citation:
ama: Burban I, Henrich T. Vector bundles on plane cubic curves and the classical
Yang-Baxter equation. Journal of the European Math Society. 2015;17(3):591–
644. doi:10.4171/JEMS/512
apa: Burban, I., & Henrich, T. (2015). Vector bundles on plane cubic curves
and the classical Yang-Baxter equation. Journal of the European Math. Society,
17(3), 591– 644. https://doi.org/10.4171/JEMS/512
bibtex: '@article{Burban_Henrich_2015, title={Vector bundles on plane cubic curves
and the classical Yang-Baxter equation}, volume={17}, DOI={10.4171/JEMS/512},
number={3}, journal={Journal of the European Math. Society}, author={Burban, Igor
and Henrich, T.}, year={2015}, pages={591– 644} }'
chicago: 'Burban, Igor, and T. Henrich. “Vector Bundles on Plane Cubic Curves and
the Classical Yang-Baxter Equation.” Journal of the European Math. Society
17, no. 3 (2015): 591– 644. https://doi.org/10.4171/JEMS/512.'
ieee: 'I. Burban and T. Henrich, “Vector bundles on plane cubic curves and the classical
Yang-Baxter equation,” Journal of the European Math. Society, vol. 17,
no. 3, pp. 591– 644, 2015, doi: 10.4171/JEMS/512.'
mla: Burban, Igor, and T. Henrich. “Vector Bundles on Plane Cubic Curves and the
Classical Yang-Baxter Equation.” Journal of the European Math. Society,
vol. 17, no. 3, 2015, pp. 591– 644, doi:10.4171/JEMS/512.
short: I. Burban, T. Henrich, Journal of the European Math. Society 17 (2015) 591–
644.
date_created: 2023-05-03T00:23:15Z
date_updated: 2023-05-07T01:34:27Z
department:
- _id: '602'
doi: 10.4171/JEMS/512
extern: '1'
intvolume: ' 17'
issue: '3'
language:
- iso: eng
page: 591– 644
publication: Journal of the European Math. Society
publication_status: published
status: public
title: Vector bundles on plane cubic curves and the classical Yang-Baxter equation
type: journal_article
user_id: '49063'
volume: 17
year: '2015'
...
---
_id: '44341'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: B.
full_name: Kreußler, B.
last_name: Kreußler
citation:
ama: Burban I, Kreußler B. Analytic moduli spaces of simple sheaves on families
of integral curves. Mathematische Nachrichten. 2014;287(2–3):173–183.
apa: Burban, I., & Kreußler, B. (2014). Analytic moduli spaces of simple sheaves
on families of integral curves. Mathematische Nachrichten, 287(2–3),
173–183.
bibtex: '@article{Burban_Kreußler_2014, title={Analytic moduli spaces of simple
sheaves on families of integral curves}, volume={287}, number={2–3}, journal={Mathematische
Nachrichten}, author={Burban, Igor and Kreußler, B.}, year={2014}, pages={173–183}
}'
chicago: 'Burban, Igor, and B. Kreußler. “Analytic Moduli Spaces of Simple Sheaves
on Families of Integral Curves.” Mathematische Nachrichten 287, no. 2–3
(2014): 173–183.'
ieee: I. Burban and B. Kreußler, “Analytic moduli spaces of simple sheaves on families
of integral curves,” Mathematische Nachrichten, vol. 287, no. 2–3, pp.
173–183, 2014.
mla: Burban, Igor, and B. Kreußler. “Analytic Moduli Spaces of Simple Sheaves on
Families of Integral Curves.” Mathematische Nachrichten, vol. 287, no.
2–3, 2014, pp. 173–183.
short: I. Burban, B. Kreußler, Mathematische Nachrichten 287 (2014) 173–183.
date_created: 2023-05-03T00:24:25Z
date_updated: 2023-05-07T01:42:01Z
department:
- _id: '602'
extern: '1'
intvolume: ' 287'
issue: 2–3
language:
- iso: eng
page: 173–183
publication: Mathematische Nachrichten
publication_status: published
status: public
title: Analytic moduli spaces of simple sheaves on families of integral curves
type: journal_article
user_id: '49063'
volume: 287
year: '2014'
...
---
_id: '44342'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: ' O.'
full_name: Schiffmann, O.
last_name: Schiffmann
citation:
ama: Burban I, Schiffmann O. Composition algebra of a weighted projective line.
Journal für Reine und Angew Mathematik. 2013;679:75–124.
apa: Burban, I., & Schiffmann, O. (2013). Composition algebra of a weighted
projective line. Journal Für Reine Und Angew. Mathematik, 679, 75–124.
bibtex: '@article{Burban_Schiffmann_2013, title={Composition algebra of a weighted
projective line}, volume={679}, journal={Journal für Reine und Angew. Mathematik},
author={Burban, Igor and Schiffmann, O.}, year={2013}, pages={75–124} }'
chicago: 'Burban, Igor, and O. Schiffmann. “Composition Algebra of a Weighted Projective
Line.” Journal Für Reine Und Angew. Mathematik 679 (2013): 75–124.'
ieee: I. Burban and O. Schiffmann, “Composition algebra of a weighted projective
line,” Journal für Reine und Angew. Mathematik, vol. 679, pp. 75–124, 2013.
mla: Burban, Igor, and O. Schiffmann. “Composition Algebra of a Weighted Projective
Line.” Journal Für Reine Und Angew. Mathematik, vol. 679, 2013, pp. 75–124.
short: I. Burban, O. Schiffmann, Journal Für Reine Und Angew. Mathematik 679 (2013)
75–124.
date_created: 2023-05-03T00:26:42Z
date_updated: 2023-05-07T01:40:36Z
department:
- _id: '602'
extern: '1'
intvolume: ' 679'
language:
- iso: eng
page: 75–124
publication: Journal für Reine und Angew. Mathematik
publication_status: published
status: public
title: Composition algebra of a weighted projective line
type: journal_article
user_id: '49063'
volume: 679
year: '2013'
...
---
_id: '44346'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: B.
full_name: Kreußler, B.
last_name: Kreußler
citation:
ama: Burban I, Kreußler B. Vector Bundles on Degenerations of Elliptic Curves
and Yang-Baxter Equations. Vol 220. 1035th ed.; 2012. doi:10.1090/S0065-9266-2012-00654-X
apa: Burban, I., & Kreußler, B. (2012). Vector bundles on degenerations of
elliptic curves and Yang-Baxter equations (1035th ed., Vol. 220). https://doi.org/10.1090/S0065-9266-2012-00654-X
bibtex: '@book{Burban_Kreußler_2012, edition={1035}, series={Memoirs of the American
Mathematical Society}, title={Vector bundles on degenerations of elliptic curves
and Yang-Baxter equations}, volume={220}, DOI={10.1090/S0065-9266-2012-00654-X},
author={Burban, Igor and Kreußler, B.}, year={2012}, collection={Memoirs of the
American Mathematical Society} }'
chicago: Burban, Igor, and B. Kreußler. Vector Bundles on Degenerations of Elliptic
Curves and Yang-Baxter Equations. 1035th ed. Vol. 220. Memoirs of the American
Mathematical Society, 2012. https://doi.org/10.1090/S0065-9266-2012-00654-X.
ieee: I. Burban and B. Kreußler, Vector bundles on degenerations of elliptic
curves and Yang-Baxter equations, 1035th ed., vol. 220. 2012.
mla: Burban, Igor, and B. Kreußler. Vector Bundles on Degenerations of Elliptic
Curves and Yang-Baxter Equations. 1035th ed., vol. 220, 2012, doi:10.1090/S0065-9266-2012-00654-X.
short: I. Burban, B. Kreußler, Vector Bundles on Degenerations of Elliptic Curves
and Yang-Baxter Equations, 1035th ed., 2012.
date_created: 2023-05-03T00:31:35Z
date_updated: 2023-05-07T01:34:10Z
department:
- _id: '602'
doi: 10.1090/S0065-9266-2012-00654-X
edition: '1035'
extern: '1'
intvolume: ' 220'
language:
- iso: eng
publication_identifier:
isbn:
- 978-0-8218-7292-5
publication_status: published
series_title: Memoirs of the American Mathematical Society
status: public
title: Vector bundles on degenerations of elliptic curves and Yang-Baxter equations
type: book
user_id: '49063'
volume: 220
year: '2012'
...
---
_id: '44344'
author:
- first_name: Igor
full_name: Burban, Igor
id: '72064'
last_name: Burban
- first_name: O.
full_name: Schiffmann, O.
last_name: Schiffmann
citation:
ama: Burban I, Schiffmann O. On the Hall algebra of an elliptic curve I. Duke
Mathematical Journal. 2012;161(7):1171–1231. doi:10.1215/00127094-1593263
apa: Burban, I., & Schiffmann, O. (2012). On the Hall algebra of an elliptic
curve I. Duke Mathematical Journal, 161(7), 1171–1231. https://doi.org/10.1215/00127094-1593263
bibtex: '@article{Burban_Schiffmann_2012, title={On the Hall algebra of an elliptic
curve I}, volume={161}, DOI={10.1215/00127094-1593263},
number={7}, journal={Duke Mathematical Journal}, author={Burban, Igor and Schiffmann,
O.}, year={2012}, pages={1171–1231} }'
chicago: 'Burban, Igor, and O. Schiffmann. “On the Hall Algebra of an Elliptic Curve
I.” Duke Mathematical Journal 161, no. 7 (2012): 1171–1231. https://doi.org/10.1215/00127094-1593263.'
ieee: 'I. Burban and O. Schiffmann, “On the Hall algebra of an elliptic curve I,”
Duke Mathematical Journal, vol. 161, no. 7, pp. 1171–1231, 2012, doi: 10.1215/00127094-1593263.'
mla: Burban, Igor, and O. Schiffmann. “On the Hall Algebra of an Elliptic Curve
I.” Duke Mathematical Journal, vol. 161, no. 7, 2012, pp. 1171–1231, doi:10.1215/00127094-1593263.
short: I. Burban, O. Schiffmann, Duke Mathematical Journal 161 (2012) 1171–1231.
date_created: 2023-05-03T00:29:04Z
date_updated: 2023-05-07T01:32:51Z
department:
- _id: '602'
doi: 10.1215/00127094-1593263
extern: '1'
intvolume: ' 161'
issue: '7'
language:
- iso: eng
page: 1171–1231
publication: Duke Mathematical Journal
publication_status: published
status: public
title: On the Hall algebra of an elliptic curve I
type: journal_article
user_id: '49063'
volume: 161
year: '2012'
...