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45 Publications
2022 | Journal Article | LibreCat-ID: 44328
Morita theory for non-commutative noetherian schemes
I. Burban, Yu. Drozd, Advances in Mathematics 399 (2022).
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| DOI
I. Burban, Yu. Drozd, Advances in Mathematics 399 (2022).
2022 | Preprint | LibreCat-ID: 44537
A classification of polyharmonic Maa forms via quiver representations
I. Burban, C. Alfes-Neumann, M. Raum, (2022).
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I. Burban, C. Alfes-Neumann, M. Raum, (2022).
2022 | Journal Article | LibreCat-ID: 44327
On elliptic solutions of the associative Yang-Baxter equation
I. Burban, A. Peruzzi, Journal of Geometry and Physics 176 (2022).
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I. Burban, A. Peruzzi, Journal of Geometry and Physics 176 (2022).
2021 | Journal Article | LibreCat-ID: 44329
Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation
I. Burban, R. Abedin, Communications in Mathematical Physics 387 (2021) 1051–1109.
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| DOI
I. Burban, R. Abedin, Communications in Mathematical Physics 387 (2021) 1051–1109.
2020 | Journal Article | LibreCat-ID: 44331
Cohen-Macaulay modules over the algebra of planar quasi-invariants and Calogero-Moser systems
I. Burban, A. Zheglov, Proceedings of the London Mathematical Society 121 (2020) 1033–1082.
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| DOI
I. Burban, A. Zheglov, Proceedings of the London Mathematical Society 121 (2020) 1033–1082.
2018 | Journal Article | LibreCat-ID: 44333
Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter equation
I. Burban, L. Galinat, Communications in Mathematical Physics 364 (2018) 123–169.
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| DOI
I. Burban, L. Galinat, Communications in Mathematical Physics 364 (2018) 123–169.
2018 | Preprint | LibreCat-ID: 44538
Non-commutative nodal curves and derived tame algebras
I. Burban, Yu. Drozd, (2018).
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I. Burban, Yu. Drozd, (2018).
2018 | Journal Article | LibreCat-ID: 44332
Fourier-Mukai transform on Weierstraß cubics and commuting differential operators
I. Burban, A. Zheglov, International Journal of Mathematics 29 (2018).
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I. Burban, A. Zheglov, International Journal of Mathematics 29 (2018).
2017 | Book | LibreCat-ID: 44337
Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems
I. Burban, Yu. Drozd, Maximal Cohen-Macaulay Modules over Non-Isolated Surface Singularities and Matrix Problems, 1178th ed., 2017.
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| DOI
I. Burban, Yu. Drozd, Maximal Cohen-Macaulay Modules over Non-Isolated Surface Singularities and Matrix Problems, 1178th ed., 2017.
2017 | Preprint | LibreCat-ID: 44539
On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems
I. Burban, Yu. Drozd, (2017).
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I. Burban, Yu. Drozd, (2017).
2017 | Journal Article | LibreCat-ID: 44334
Simple vector bundles on a nodal Weierstraß cubic and quasi-trigonometric solutions of CYBE
I. Burban, L. Galinat, Journal of Physics A: Mathematical and Theoretical 50 (2017).
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I. Burban, L. Galinat, Journal of Physics A: Mathematical and Theoretical 50 (2017).
2017 | Journal Article | LibreCat-ID: 44335
Minors of non-commutative schemes
I. Burban, Yu. Drozd, V. Gavran, European Journal of Mathematics 3 (2017) 311–341.
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I. Burban, Yu. Drozd, V. Gavran, European Journal of Mathematics 3 (2017) 311–341.
2017 | Journal Article | LibreCat-ID: 44336
Singular curves and quasi–hereditary algebras
I. Burban, Yu. Drozd, V. Gavran, International Mathematics Research Notices 2017 (2017) 895–920.
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I. Burban, Yu. Drozd, V. Gavran, International Mathematics Research Notices 2017 (2017) 895–920.
2016 | Journal Article | LibreCat-ID: 44339
Cohen-Macaulay modules over some non-reduced curve singularities
I. Burban, W. Gnedin, Journal of Pure and Applied Algebra 220 (2016) 3777–3815.
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I. Burban, W. Gnedin, Journal of Pure and Applied Algebra 220 (2016) 3777–3815.
2015 | Journal Article | LibreCat-ID: 44340
Vector bundles on plane cubic curves and the classical Yang-Baxter equation
I. Burban, T. Henrich, Journal of the European Math. Society 17 (2015) 591– 644.
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| DOI
I. Burban, T. Henrich, Journal of the European Math. Society 17 (2015) 591– 644.
2014 | Journal Article | LibreCat-ID: 44341
Analytic moduli spaces of simple sheaves on families of integral curves
I. Burban, B. Kreußler, Mathematische Nachrichten 287 (2014) 173–183.
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I. Burban, B. Kreußler, Mathematische Nachrichten 287 (2014) 173–183.
2013 | Journal Article | LibreCat-ID: 44342
Composition algebra of a weighted projective line
I. Burban, O. Schiffmann, Journal Für Reine Und Angew. Mathematik 679 (2013) 75–124.
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I. Burban, O. Schiffmann, Journal Für Reine Und Angew. Mathematik 679 (2013) 75–124.
2012 | Book | LibreCat-ID: 44346
Vector bundles on degenerations of elliptic curves and Yang-Baxter equations
I. Burban, B. Kreußler, Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations, 1035th ed., 2012.
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| DOI
I. Burban, B. Kreußler, Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations, 1035th ed., 2012.
2012 | Journal Article | LibreCat-ID: 44344
On the Hall algebra of an elliptic curve I
I. Burban, O. Schiffmann, Duke Mathematical Journal 161 (2012) 1171–1231.
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| DOI
I. Burban, O. Schiffmann, Duke Mathematical Journal 161 (2012) 1171–1231.
2012 | Journal Article | LibreCat-ID: 44345
Semi-stable vector bundles on elliptic curves and the associative Yang-Baxter equation
I. Burban, T. Henrich, Journal of Geometry and Physics 62 (2012) 312–329.
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I. Burban, T. Henrich, Journal of Geometry and Physics 62 (2012) 312–329.
2012 | Journal Article | LibreCat-ID: 44347
Two descriptions of the quantum affine algebra Uv(sl2) via Hall algebra approach
I. Burban, O. Schiffmann, Glasgow Journal of Math. 54 (2012) 283–307.
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I. Burban, O. Schiffmann, Glasgow Journal of Math. 54 (2012) 283–307.
2012 | Journal Article | LibreCat-ID: 44348
Frobenius morphism and vector bundles on cycles of projective lines
I. Burban, Communications in Algebra 40 (2012) 2983–2988.
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I. Burban, Communications in Algebra 40 (2012) 2983–2988.
2012 | Journal Article | LibreCat-ID: 44343
Singularity category of a non–commutative resolution of singularities
I. Burban, M. Kalck, Advances in Mathematics 231 (2012) 414–435.
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I. Burban, M. Kalck, Advances in Mathematics 231 (2012) 414–435.
2011 | Journal Article | LibreCat-ID: 44349
Tilting on non–commutative rational projective curves
I. Burban, Yu. Drozd, Mathematische Annalen 351 (2011) 665–709.
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I. Burban, Yu. Drozd, Mathematische Annalen 351 (2011) 665–709.
2008 | Journal Article | LibreCat-ID: 44350
Cluster tilting for one–dimensional hypersurface singularities
I. Burban, O. Iyama, B. Keller, I. Reiten, Advances in Mathematics 217 (2008) 2443–2484.
LibreCat
| DOI
I. Burban, O. Iyama, B. Keller, I. Reiten, Advances in Mathematics 217 (2008) 2443–2484.
2008 | Book Chapter | LibreCat-ID: 44530
Maximal Cohen-Macaulay modules over surface singularities
I. Burban, Yu. Drozd, in: Trends in Representations of Algebras and Related Topics, EMS Publishing House, 2008, pp. 101–160.
LibreCat
I. Burban, Yu. Drozd, in: Trends in Representations of Algebras and Related Topics, EMS Publishing House, 2008, pp. 101–160.
2006 | Book Chapter | LibreCat-ID: 44531
Vector bundles and torsion free sheaves on degenerations of elliptic curves
I. Burban, L. Bodnarchuk, Yu. Drozd, G.-M. Greuel, in: Global Aspects of Complex Geometry, Springer, 2006, pp. 83–129.
LibreCat
I. Burban, L. Bodnarchuk, Yu. Drozd, G.-M. Greuel, in: Global Aspects of Complex Geometry, Springer, 2006, pp. 83–129.
2006 | Journal Article | LibreCat-ID: 44352
On a relative Fourier–Mukai transform on genus one fibrations
I. Burban, B. Kreußler, Manuscripta Mathematica 120 (2006) 283–306.
LibreCat
I. Burban, B. Kreußler, Manuscripta Mathematica 120 (2006) 283–306.
2006 | Journal Article | LibreCat-ID: 44351
Derived categories of irreducible projective curves of arithmetic genus one
I. Burban, B. Kreußler, Compositio Mathematica 142 (2006) 1231–1262.
LibreCat
I. Burban, B. Kreußler, Compositio Mathematica 142 (2006) 1231–1262.
2005 | Book Chapter | LibreCat-ID: 44532
Derived categories for nodal rings and projective configurations, Noncommutative Algebra and Geometry
I. Burban, Yu. Drozd, in: A Series of Lecture Notes in Pure and Applied Mathematics, 2005, pp. 23–46.
LibreCat
I. Burban, Yu. Drozd, in: A Series of Lecture Notes in Pure and Applied Mathematics, 2005, pp. 23–46.
2005 | Journal Article | LibreCat-ID: 44354
Derived Categories and D-Branes
I. Burban, Ukrain. Mat. Zh. 57 (2005).
LibreCat
I. Burban, Ukrain. Mat. Zh. 57 (2005).
2005 | Journal Article | LibreCat-ID: 44353
Fourier-Mukai transforms and semi-stable sheaves on nodal Weierstraß cubics
I. Burban, B. Kreußler, J. Reine Angew. Math. 584 (2005) 45–82.
LibreCat
I. Burban, B. Kreußler, J. Reine Angew. Math. 584 (2005) 45–82.
2004 | Journal Article | LibreCat-ID: 44355
Coherent sheaves on rational curves with simple double points and transversal intersections
I. Burban, Yu. Drozd, Duke Mathematical Journal 121 (2004) 189–229.
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| DOI
I. Burban, Yu. Drozd, Duke Mathematical Journal 121 (2004) 189–229.
2004 | Conference Paper | LibreCat-ID: 44533
Indecomposables of the derived categories of certain associative algebras
I. Burban, Yu. Drozd, in: Proceedings of the ICRA-X Conference, Toronto 2002, 2004, pp. 109–127.
LibreCat
I. Burban, Yu. Drozd, in: Proceedings of the ICRA-X Conference, Toronto 2002, 2004, pp. 109–127.
2004 | Book Chapter | LibreCat-ID: 44534
Derived categories of coherent sheaves on rational singular curves
I. Burban, in: Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry, American Mathematical Society, 2004, pp. 173–188.
LibreCat
I. Burban, in: Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry, American Mathematical Society, 2004, pp. 173–188.
2004 | Journal Article | LibreCat-ID: 44356
Derived tameness of nodal algebras
I. Burban, Yu. Drozd, J. Algebra 272 (2004) 46–94.
LibreCat
I. Burban, Yu. Drozd, J. Algebra 272 (2004) 46–94.
2003 | Journal Article | LibreCat-ID: 44357
Stable vector bundles on a rational curve with one node
I. Burban, Ukrain. Mat. Zh. 55 (2003) 867–874.
LibreCat
I. Burban, Ukrain. Mat. Zh. 55 (2003) 867–874.
2002 | Conference Paper | LibreCat-ID: 44535
Derived categories and matrix problems
I. Burban, Yu. Drozd, in: Ukrainian Mathematical Congress 2001. Algebraic Structures and Their Applications. Proceedings of the Third International Algebraic Conference Held in Framework of the Ukrainian Mathematical Congress, Instytut Matematyky NAN Ukrainy, Kyiv, 2002, pp. 201–211.
LibreCat
I. Burban, Yu. Drozd, in: Ukrainian Mathematical Congress 2001. Algebraic Structures and Their Applications. Proceedings of the Third International Algebraic Conference Held in Framework of the Ukrainian Mathematical Congress, Instytut Matematyky NAN Ukrainy, Kyiv, 2002, pp. 201–211.
2002 | Journal Article | LibreCat-ID: 44358
Geometrical properties of sections of Buchsbaum- Rim sheaves
I. Burban, H.-G. Freiermuth, Le Matematiche LVII (2002) 265–283.
LibreCat
I. Burban, H.-G. Freiermuth, Le Matematiche LVII (2002) 265–283.
2001 | Book Chapter | LibreCat-ID: 44536
Vector bundles on singular projective curves
I. Burban, Yu. Drozd, G.-M. Greuel, in: C. Ciliberto (Ed.), Applications of Algebraic Geometry to Coding Theory, Physics and Computation, Kluwer Academic Publishers, 2001, pp. 1–15.
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I. Burban, Yu. Drozd, G.-M. Greuel, in: C. Ciliberto (Ed.), Applications of Algebraic Geometry to Coding Theory, Physics and Computation, Kluwer Academic Publishers, 2001, pp. 1–15.
1998 | Journal Article | LibreCat-ID: 44541
Projective transformations of a plane
I. Burban, W. Duma, U Sviti Mathematyky 4 (1998).
LibreCat
I. Burban, W. Duma, U Sviti Mathematyky 4 (1998).
1998 | Journal Article | LibreCat-ID: 44540
Projective transformations of a plane and three-dimensional space
I. Burban, W. Duma, U Sviti Mathematyky 4 (1998).
LibreCat
I. Burban, W. Duma, U Sviti Mathematyky 4 (1998).
1998 | Journal Article | LibreCat-ID: 44542
Rational parameterization of algebraic curves
I. Burban, U Sviti Mathematyky 4 (1998).
LibreCat
I. Burban, U Sviti Mathematyky 4 (1998).
1996 | Journal Article | LibreCat-ID: 44544
Euler’s theorem and map color problems
I. Burban, U Sviti Mathematyky 2 (1996).
LibreCat
I. Burban, U Sviti Mathematyky 2 (1996).
1996 | Journal Article | LibreCat-ID: 44543
Solutions of equations in integers
I. Burban, U Sviti Mathematyky 2 (1996).
LibreCat
I. Burban, U Sviti Mathematyky 2 (1996).