45 Publications
2022 | Journal Article | LibreCat-ID: 44328
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.
LibreCat
| DOI
2022 | Preprint | LibreCat-ID: 44537
I. Burban, C. Alfes-Neumann, and M. Raum, “A classification of polyharmonic Maa forms via quiver representations.” 2022.
LibreCat
| Download (ext.)
2022 | Journal Article | LibreCat-ID: 44327
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.
LibreCat
2021 | Journal Article | LibreCat-ID: 44329
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.
LibreCat
| DOI
2020 | Journal Article | LibreCat-ID: 44331
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.
LibreCat
| DOI
2018 | Journal Article | LibreCat-ID: 44333
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.
LibreCat
| DOI
2018 | Preprint | LibreCat-ID: 44538
I. Burban and Yu. Drozd, “Non-commutative nodal curves and derived tame algebras.” 2018.
LibreCat
| Download (ext.)
2018 | Journal Article | LibreCat-ID: 44332
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.
LibreCat
2017 | Preprint | LibreCat-ID: 44539
I. Burban and Yu. Drozd, “On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems.” 2017.
LibreCat
| Download (ext.)
2017 | Journal Article | LibreCat-ID: 44334
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.
LibreCat
2017 | Journal Article | LibreCat-ID: 44335
I. Burban, Yu. Drozd, and V. Gavran, “Minors of non-commutative schemes,” European Journal of Mathematics, vol. 3, no. 2, pp. 311–341, 2017.
LibreCat
2017 | Journal Article | LibreCat-ID: 44336
I. Burban, Yu. Drozd, and V. Gavran, “Singular curves and quasi–hereditary algebras,” International Mathematics Research Notices 2017, no. 3, pp. 895–920, 2017.
LibreCat
2016 | Journal Article | LibreCat-ID: 44339
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.
LibreCat
2015 | Journal Article | LibreCat-ID: 44340
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.
LibreCat
| DOI
2014 | Journal Article | LibreCat-ID: 44341
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.
LibreCat
2013 | Journal Article | LibreCat-ID: 44342
I. Burban and O. Schiffmann, “Composition algebra of a weighted projective line,” Journal für Reine und Angew. Mathematik, vol. 679, pp. 75–124, 2013.
LibreCat
2012 | Journal Article | LibreCat-ID: 44344
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.
LibreCat
| DOI
2012 | Journal Article | LibreCat-ID: 44345
I. Burban and T. Henrich, “Semi-stable vector bundles on elliptic curves and the associative Yang-Baxter equation,” Journal of Geometry and Physics, vol. 62, no. 2, pp. 312–329, 2012.
LibreCat
2012 | Journal Article | LibreCat-ID: 44347
I. Burban and O. Schiffmann, “Two descriptions of the quantum affine algebra Uv(sl2) via Hall algebra approach,” Glasgow Journal of Math., vol. 54, no. 2, pp. 283–307, 2012.
LibreCat
2012 | Journal Article | LibreCat-ID: 44348
I. Burban, “Frobenius morphism and vector bundles on cycles of projective lines,” Communications in Algebra, vol. 40, no. 8, pp. 2983–2988, 2012.
LibreCat
2012 | Journal Article | LibreCat-ID: 44343
I. Burban and M. Kalck, “Singularity category of a non–commutative resolution of singularities,” Advances in Mathematics, vol. 231, no. 1, pp. 414–435, 2012.
LibreCat
2011 | Journal Article | LibreCat-ID: 44349
I. Burban and Yu. Drozd, “Tilting on non–commutative rational projective curves,” Mathematische Annalen, vol. 351, no. 3, pp. 665–709, 2011.
LibreCat
2008 | Journal Article | LibreCat-ID: 44350
I. Burban, O. Iyama, B. Keller, and I. Reiten, “Cluster tilting for one–dimensional hypersurface singularities,” Advances in Mathematics, vol. 217, no. 6, pp. 2443–2484, 2008, doi: 10.1016/j.aim.2007.10.007.
LibreCat
| DOI
2008 | Book Chapter | LibreCat-ID: 44530
I. Burban and Yu. Drozd, “Maximal Cohen-Macaulay modules over surface singularities,” in Trends in Representations of Algebras and Related Topics, EMS Publishing House, 2008, pp. 101–160.
LibreCat
2006 | Book Chapter | LibreCat-ID: 44531
I. Burban, L. Bodnarchuk, Yu. Drozd, and G.-M. Greuel, “Vector bundles and torsion free sheaves on degenerations of elliptic curves,” in Global Aspects of Complex Geometry, Springer, 2006, pp. 83–129.
LibreCat
2006 | Journal Article | LibreCat-ID: 44352
I. Burban and B. Kreußler, “On a relative Fourier–Mukai transform on genus one fibrations,” manuscripta mathematica, vol. 120, no. 3, pp. 283–306, 2006.
LibreCat
2006 | Journal Article | LibreCat-ID: 44351
I. Burban and B. Kreußler, “Derived categories of irreducible projective curves of arithmetic genus one,” Compositio Mathematica, vol. 142, pp. 1231–1262, 2006.
LibreCat
2005 | Book Chapter | LibreCat-ID: 44532
I. Burban and Yu. Drozd, “Derived categories for nodal rings and projective configurations, Noncommutative Algebra and Geometry,” in A series of Lecture Notes in Pure and Applied Mathematics, vol. 243, 2005, pp. 23–46.
LibreCat
2005 | Journal Article | LibreCat-ID: 44354
I. Burban, “Derived Categories and D-Branes,” Ukrain. Mat. Zh., vol. 57, no. 1, 2005.
LibreCat
2005 | Journal Article | LibreCat-ID: 44353
I. Burban and B. Kreußler, “Fourier-Mukai transforms and semi-stable sheaves on nodal Weierstraß cubics,” J. Reine Angew. Math., vol. 584, pp. 45–82, 2005.
LibreCat
2004 | Journal Article | LibreCat-ID: 44355
I. Burban and Yu. Drozd, “Coherent sheaves on rational curves with simple double points and transversal intersections,” Duke Mathematical Journal, vol. 121, no. 2, pp. 189–229, 2004, doi: 10.1215/S0012-7094-04-12121-9.
LibreCat
| DOI
2004 | Conference Paper | LibreCat-ID: 44533
I. Burban and Yu. Drozd, “Indecomposables of the derived categories of certain associative algebras,” in Proceedings of the ICRA-X Conference, Toronto 2002, Toronto, 2004, vol. 45, pp. 109–127.
LibreCat
2004 | Book Chapter | LibreCat-ID: 44534
I. Burban, “Derived categories of coherent sheaves on rational singular curves,” in Representations of finite dimensional algebras and related topics in Lie theory and geometry, vol. 40, American Mathematical Society, 2004, pp. 173–188.
LibreCat
2004 | Journal Article | LibreCat-ID: 44356
I. Burban and Yu. Drozd, “Derived tameness of nodal algebras,” J. Algebra, vol. 272, no. 1, pp. 46–94, 2004.
LibreCat
2003 | Journal Article | LibreCat-ID: 44357
I. Burban, “Stable vector bundles on a rational curve with one node,” Ukrain. Mat. Zh., vol. 55, no. 7, pp. 867–874, 2003.
LibreCat
2002 | Conference Paper | LibreCat-ID: 44535
I. Burban and Yu. Drozd, “Derived categories and matrix problems,” 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, Kiev, Ukraine, 2002, pp. 201–211.
LibreCat
2002 | Journal Article | LibreCat-ID: 44358
I. Burban and H.-G. Freiermuth, “Geometrical properties of sections of Buchsbaum- Rim sheaves,” Le Matematiche, vol. LVII, pp. 265–283, 2002.
LibreCat
2001 | Book Chapter | LibreCat-ID: 44536
I. Burban, Yu. Drozd, and G.-M. Greuel, “Vector bundles on singular projective curves,” in Applications of algebraic geometry to coding theory, physics and computation, C. Ciliberto, Ed. Kluwer Academic Publishers, 2001, pp. 1–15.
LibreCat
1998 | Journal Article | LibreCat-ID: 44541
I. Burban and W. Duma, “Projective transformations of a plane,” U sviti Mathematyky, vol. 4, no. 2, 1998.
LibreCat
1998 | Journal Article | LibreCat-ID: 44540
I. Burban and W. Duma, “Projective transformations of a plane and three-dimensional space,” U sviti Mathematyky, vol. 4, no. 4, 1998.
LibreCat
1998 | Journal Article | LibreCat-ID: 44542
I. Burban, “Rational parameterization of algebraic curves,” U sviti Mathematyky, vol. 4, no. 1, 1998.
LibreCat
1996 | Journal Article | LibreCat-ID: 44544
I. Burban, “Euler’s theorem and map color problems,” U sviti Mathematyky, vol. 2, no. 2, 1996.
LibreCat
1996 | Journal Article | LibreCat-ID: 44543
I. Burban, “Solutions of equations in integers,” U sviti Mathematyky, vol. 2, no. 4, 1996.
LibreCat
45 Publications
2022 | Journal Article | LibreCat-ID: 44328
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.
LibreCat
| DOI
2022 | Preprint | LibreCat-ID: 44537
I. Burban, C. Alfes-Neumann, and M. Raum, “A classification of polyharmonic Maa forms via quiver representations.” 2022.
LibreCat
| Download (ext.)
2022 | Journal Article | LibreCat-ID: 44327
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.
LibreCat
2021 | Journal Article | LibreCat-ID: 44329
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.
LibreCat
| DOI
2020 | Journal Article | LibreCat-ID: 44331
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.
LibreCat
| DOI
2018 | Journal Article | LibreCat-ID: 44333
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.
LibreCat
| DOI
2018 | Preprint | LibreCat-ID: 44538
I. Burban and Yu. Drozd, “Non-commutative nodal curves and derived tame algebras.” 2018.
LibreCat
| Download (ext.)
2018 | Journal Article | LibreCat-ID: 44332
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.
LibreCat
2017 | Preprint | LibreCat-ID: 44539
I. Burban and Yu. Drozd, “On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems.” 2017.
LibreCat
| Download (ext.)
2017 | Journal Article | LibreCat-ID: 44334
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.
LibreCat
2017 | Journal Article | LibreCat-ID: 44335
I. Burban, Yu. Drozd, and V. Gavran, “Minors of non-commutative schemes,” European Journal of Mathematics, vol. 3, no. 2, pp. 311–341, 2017.
LibreCat
2017 | Journal Article | LibreCat-ID: 44336
I. Burban, Yu. Drozd, and V. Gavran, “Singular curves and quasi–hereditary algebras,” International Mathematics Research Notices 2017, no. 3, pp. 895–920, 2017.
LibreCat
2016 | Journal Article | LibreCat-ID: 44339
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.
LibreCat
2015 | Journal Article | LibreCat-ID: 44340
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.
LibreCat
| DOI
2014 | Journal Article | LibreCat-ID: 44341
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.
LibreCat
2013 | Journal Article | LibreCat-ID: 44342
I. Burban and O. Schiffmann, “Composition algebra of a weighted projective line,” Journal für Reine und Angew. Mathematik, vol. 679, pp. 75–124, 2013.
LibreCat
2012 | Journal Article | LibreCat-ID: 44344
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.
LibreCat
| DOI
2012 | Journal Article | LibreCat-ID: 44345
I. Burban and T. Henrich, “Semi-stable vector bundles on elliptic curves and the associative Yang-Baxter equation,” Journal of Geometry and Physics, vol. 62, no. 2, pp. 312–329, 2012.
LibreCat
2012 | Journal Article | LibreCat-ID: 44347
I. Burban and O. Schiffmann, “Two descriptions of the quantum affine algebra Uv(sl2) via Hall algebra approach,” Glasgow Journal of Math., vol. 54, no. 2, pp. 283–307, 2012.
LibreCat
2012 | Journal Article | LibreCat-ID: 44348
I. Burban, “Frobenius morphism and vector bundles on cycles of projective lines,” Communications in Algebra, vol. 40, no. 8, pp. 2983–2988, 2012.
LibreCat
2012 | Journal Article | LibreCat-ID: 44343
I. Burban and M. Kalck, “Singularity category of a non–commutative resolution of singularities,” Advances in Mathematics, vol. 231, no. 1, pp. 414–435, 2012.
LibreCat
2011 | Journal Article | LibreCat-ID: 44349
I. Burban and Yu. Drozd, “Tilting on non–commutative rational projective curves,” Mathematische Annalen, vol. 351, no. 3, pp. 665–709, 2011.
LibreCat
2008 | Journal Article | LibreCat-ID: 44350
I. Burban, O. Iyama, B. Keller, and I. Reiten, “Cluster tilting for one–dimensional hypersurface singularities,” Advances in Mathematics, vol. 217, no. 6, pp. 2443–2484, 2008, doi: 10.1016/j.aim.2007.10.007.
LibreCat
| DOI
2008 | Book Chapter | LibreCat-ID: 44530
I. Burban and Yu. Drozd, “Maximal Cohen-Macaulay modules over surface singularities,” in Trends in Representations of Algebras and Related Topics, EMS Publishing House, 2008, pp. 101–160.
LibreCat
2006 | Book Chapter | LibreCat-ID: 44531
I. Burban, L. Bodnarchuk, Yu. Drozd, and G.-M. Greuel, “Vector bundles and torsion free sheaves on degenerations of elliptic curves,” in Global Aspects of Complex Geometry, Springer, 2006, pp. 83–129.
LibreCat
2006 | Journal Article | LibreCat-ID: 44352
I. Burban and B. Kreußler, “On a relative Fourier–Mukai transform on genus one fibrations,” manuscripta mathematica, vol. 120, no. 3, pp. 283–306, 2006.
LibreCat
2006 | Journal Article | LibreCat-ID: 44351
I. Burban and B. Kreußler, “Derived categories of irreducible projective curves of arithmetic genus one,” Compositio Mathematica, vol. 142, pp. 1231–1262, 2006.
LibreCat
2005 | Book Chapter | LibreCat-ID: 44532
I. Burban and Yu. Drozd, “Derived categories for nodal rings and projective configurations, Noncommutative Algebra and Geometry,” in A series of Lecture Notes in Pure and Applied Mathematics, vol. 243, 2005, pp. 23–46.
LibreCat
2005 | Journal Article | LibreCat-ID: 44354
I. Burban, “Derived Categories and D-Branes,” Ukrain. Mat. Zh., vol. 57, no. 1, 2005.
LibreCat
2005 | Journal Article | LibreCat-ID: 44353
I. Burban and B. Kreußler, “Fourier-Mukai transforms and semi-stable sheaves on nodal Weierstraß cubics,” J. Reine Angew. Math., vol. 584, pp. 45–82, 2005.
LibreCat
2004 | Journal Article | LibreCat-ID: 44355
I. Burban and Yu. Drozd, “Coherent sheaves on rational curves with simple double points and transversal intersections,” Duke Mathematical Journal, vol. 121, no. 2, pp. 189–229, 2004, doi: 10.1215/S0012-7094-04-12121-9.
LibreCat
| DOI
2004 | Conference Paper | LibreCat-ID: 44533
I. Burban and Yu. Drozd, “Indecomposables of the derived categories of certain associative algebras,” in Proceedings of the ICRA-X Conference, Toronto 2002, Toronto, 2004, vol. 45, pp. 109–127.
LibreCat
2004 | Book Chapter | LibreCat-ID: 44534
I. Burban, “Derived categories of coherent sheaves on rational singular curves,” in Representations of finite dimensional algebras and related topics in Lie theory and geometry, vol. 40, American Mathematical Society, 2004, pp. 173–188.
LibreCat
2004 | Journal Article | LibreCat-ID: 44356
I. Burban and Yu. Drozd, “Derived tameness of nodal algebras,” J. Algebra, vol. 272, no. 1, pp. 46–94, 2004.
LibreCat
2003 | Journal Article | LibreCat-ID: 44357
I. Burban, “Stable vector bundles on a rational curve with one node,” Ukrain. Mat. Zh., vol. 55, no. 7, pp. 867–874, 2003.
LibreCat
2002 | Conference Paper | LibreCat-ID: 44535
I. Burban and Yu. Drozd, “Derived categories and matrix problems,” 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, Kiev, Ukraine, 2002, pp. 201–211.
LibreCat
2002 | Journal Article | LibreCat-ID: 44358
I. Burban and H.-G. Freiermuth, “Geometrical properties of sections of Buchsbaum- Rim sheaves,” Le Matematiche, vol. LVII, pp. 265–283, 2002.
LibreCat
2001 | Book Chapter | LibreCat-ID: 44536
I. Burban, Yu. Drozd, and G.-M. Greuel, “Vector bundles on singular projective curves,” in Applications of algebraic geometry to coding theory, physics and computation, C. Ciliberto, Ed. Kluwer Academic Publishers, 2001, pp. 1–15.
LibreCat
1998 | Journal Article | LibreCat-ID: 44541
I. Burban and W. Duma, “Projective transformations of a plane,” U sviti Mathematyky, vol. 4, no. 2, 1998.
LibreCat
1998 | Journal Article | LibreCat-ID: 44540
I. Burban and W. Duma, “Projective transformations of a plane and three-dimensional space,” U sviti Mathematyky, vol. 4, no. 4, 1998.
LibreCat
1998 | Journal Article | LibreCat-ID: 44542
I. Burban, “Rational parameterization of algebraic curves,” U sviti Mathematyky, vol. 4, no. 1, 1998.
LibreCat
1996 | Journal Article | LibreCat-ID: 44544
I. Burban, “Euler’s theorem and map color problems,” U sviti Mathematyky, vol. 2, no. 2, 1996.
LibreCat
1996 | Journal Article | LibreCat-ID: 44543
I. Burban, “Solutions of equations in integers,” U sviti Mathematyky, vol. 2, no. 4, 1996.
LibreCat