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45 Publications
2022 | Journal Article | LibreCat-ID: 44328
Burban I, Drozd Yu. Morita theory for non-commutative noetherian schemes. Advances in Mathematics. 2022;399. doi:10.1016/j.aim.2022.108273
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| DOI
2022 | Preprint | LibreCat-ID: 44537
Burban I, Alfes-Neumann C, Raum M. A classification of polyharmonic Maa forms via quiver representations. Published online 2022.
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2022 | Journal Article | LibreCat-ID: 44327
Burban I, Peruzzi A. On elliptic solutions of the associative Yang-Baxter equation. Journal of Geometry and Physics. 2022;176.
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2021 | Journal Article | LibreCat-ID: 44329
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
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2020 | Journal Article | LibreCat-ID: 44331
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
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2018 | Journal Article | LibreCat-ID: 44333
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
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| DOI
2018 | Preprint | LibreCat-ID: 44538
Burban I, Drozd Yu. Non-commutative nodal curves and derived tame algebras. Published online 2018.
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2018 | Journal Article | LibreCat-ID: 44332
Burban I, Zheglov A. Fourier-Mukai transform on Weierstraß cubics and commuting differential operators. International Journal of Mathematics. 2018;29(10).
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2017 | Book | LibreCat-ID: 44337
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
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| DOI
2017 | Preprint | LibreCat-ID: 44539
Burban I, Drozd Yu. On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems. Published online 2017.
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2017 | Journal Article | LibreCat-ID: 44334
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.
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2017 | Journal Article | LibreCat-ID: 44335
Burban I, Drozd Yu, Gavran V. Minors of non-commutative schemes. European Journal of Mathematics. 2017;3(2):311–341.
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2017 | Journal Article | LibreCat-ID: 44336
Burban I, Drozd Yu, Gavran V. Singular curves and quasi–hereditary algebras. International Mathematics Research Notices 2017. 2017;(3):895-920.
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2016 | Journal Article | LibreCat-ID: 44339
Burban I, Gnedin W. Cohen-Macaulay modules over some non-reduced curve singularities. Journal of Pure and Applied Algebra. 2016;220(12):3777–3815.
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2015 | Journal Article | LibreCat-ID: 44340
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
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| DOI
2014 | Journal Article | LibreCat-ID: 44341
Burban I, Kreußler B. Analytic moduli spaces of simple sheaves on families of integral curves. Mathematische Nachrichten. 2014;287(2–3):173–183.
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2013 | Journal Article | LibreCat-ID: 44342
Burban I, Schiffmann O. Composition algebra of a weighted projective line. Journal für Reine und Angew Mathematik. 2013;679:75–124.
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2012 | Book | LibreCat-ID: 44346
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
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| DOI
2012 | Journal Article | LibreCat-ID: 44344
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
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| DOI
2012 | Journal Article | LibreCat-ID: 44345
Burban I, Henrich T. Semi-stable vector bundles on elliptic curves and the associative Yang-Baxter equation. Journal of Geometry and Physics. 2012;62(2):312–329.
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2012 | Journal Article | LibreCat-ID: 44347
Burban I, Schiffmann O. Two descriptions of the quantum affine algebra Uv(sl2) via Hall algebra approach. Glasgow Journal of Math. 2012;54(2):283–307.
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2012 | Journal Article | LibreCat-ID: 44348
Burban I. Frobenius morphism and vector bundles on cycles of projective lines. Communications in Algebra. 2012;40(8):2983–2988.
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2012 | Journal Article | LibreCat-ID: 44343
Burban I, Kalck M. Singularity category of a non–commutative resolution of singularities. Advances in Mathematics. 2012;231(1):414–435.
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2011 | Journal Article | LibreCat-ID: 44349
Burban I, Drozd Yu. Tilting on non–commutative rational projective curves. Mathematische Annalen. 2011;351(3):665–709.
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2008 | Journal Article | LibreCat-ID: 44350
Burban I, Iyama O., Keller B, Reiten I. Cluster tilting for one–dimensional hypersurface singularities. Advances in Mathematics. 2008;217(6):2443–2484. doi:10.1016/j.aim.2007.10.007
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| DOI
2008 | Book Chapter | LibreCat-ID: 44530
Burban I, Drozd Yu. Maximal Cohen-Macaulay modules over surface singularities. In: Trends in Representations of Algebras and Related Topics. EMS Publishing House; 2008:101–160.
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2006 | Book Chapter | LibreCat-ID: 44531
Burban I, Bodnarchuk L, Drozd Yu, Greuel G-M. Vector bundles and torsion free sheaves on degenerations of elliptic curves. In: Global Aspects of Complex Geometry. Springer; 2006:83–129.
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2006 | Journal Article | LibreCat-ID: 44352
Burban I, Kreußler B. On a relative Fourier–Mukai transform on genus one fibrations. manuscripta mathematica. 2006;120(3):283–306.
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2006 | Journal Article | LibreCat-ID: 44351
Burban I, Kreußler B. Derived categories of irreducible projective curves of arithmetic genus one. Compositio Mathematica. 2006;142:1231–1262.
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2005 | Book Chapter | LibreCat-ID: 44532
Burban I, Drozd Yu. 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. ; 2005:23–46.
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2005 | Journal Article | LibreCat-ID: 44354
Burban I. Derived Categories and D-Branes. Ukrain Mat Zh. 2005;57(1).
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2005 | Journal Article | LibreCat-ID: 44353
Burban I, Kreußler B. Fourier-Mukai transforms and semi-stable sheaves on nodal Weierstraß cubics. J Reine Angew Math. 2005;584:45–82.
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2004 | Journal Article | LibreCat-ID: 44355
Burban I, Drozd Yu. Coherent sheaves on rational curves with simple double points and transversal intersections. Duke Mathematical Journal. 2004;121(2):189–229. doi:10.1215/S0012-7094-04-12121-9
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| DOI
2004 | Conference Paper | LibreCat-ID: 44533
Burban I, Drozd Yu. Indecomposables of the derived categories of certain associative algebras. In: Proceedings of the ICRA-X Conference, Toronto 2002. Vol 45. Fields Institute Communications. ; 2004:109–127.
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2004 | Book Chapter | LibreCat-ID: 44534
Burban I. 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. Fields Institute Communications. American Mathematical Society; 2004:173–188.
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2004 | Journal Article | LibreCat-ID: 44356
Burban I, Drozd Yu. Derived tameness of nodal algebras. J Algebra. 2004;272(1):46–94.
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2003 | Journal Article | LibreCat-ID: 44357
Burban I. Stable vector bundles on a rational curve with one node. Ukrain Mat Zh. 2003;55(7):867–874.
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2002 | Conference Paper | LibreCat-ID: 44535
Burban I, Drozd Yu. 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. Instytut Matematyky NAN Ukrainy; 2002:201-211.
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2002 | Journal Article | LibreCat-ID: 44358
Burban I, Freiermuth H-G. Geometrical properties of sections of Buchsbaum- Rim sheaves. Le Matematiche. 2002;LVII:265–283.
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2001 | Book Chapter | LibreCat-ID: 44536
Burban I, Drozd Yu, Greuel G-M. Vector bundles on singular projective curves. In: Ciliberto C, ed. Applications of Algebraic Geometry to Coding Theory, Physics and Computation. Kluwer Academic Publishers; 2001:1–15.
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1998 | Journal Article | LibreCat-ID: 44541
Burban I, Duma W. Projective transformations of a plane. U sviti Mathematyky. 1998;4(2).
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1998 | Journal Article | LibreCat-ID: 44540
Burban I, Duma W. Projective transformations of a plane and three-dimensional space. U sviti Mathematyky. 1998;4(4).
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1998 | Journal Article | LibreCat-ID: 44542
Burban I. Rational parameterization of algebraic curves. U sviti Mathematyky. 1998;4(1).
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1996 | Journal Article | LibreCat-ID: 44544
Burban I. Euler’s theorem and map color problems. U sviti Mathematyky. 1996;2(2).
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1996 | Journal Article | LibreCat-ID: 44543
Burban I. Solutions of equations in integers. U sviti Mathematyky. 1996;2(4).
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