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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.
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| DOI
2022 | Preprint | LibreCat-ID: 44537
I. Burban, C. Alfes-Neumann, and M. Raum, “A classification of polyharmonic Maa forms via quiver representations.” 2022.
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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.
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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.
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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.
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| 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.
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| DOI
2018 | Preprint | LibreCat-ID: 44538
I. Burban and Yu. Drozd, “Non-commutative nodal curves and derived tame algebras.” 2018.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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| 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.
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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.
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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.
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| 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.
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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.
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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.
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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.
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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.
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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.
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| 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.
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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.
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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.
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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.
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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.
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2005 | Journal Article | LibreCat-ID: 44354
I. Burban, “Derived Categories and D-Branes,” Ukrain. Mat. Zh., vol. 57, no. 1, 2005.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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1998 | Journal Article | LibreCat-ID: 44541
I. Burban and W. Duma, “Projective transformations of a plane,” U sviti Mathematyky, vol. 4, no. 2, 1998.
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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.
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1998 | Journal Article | LibreCat-ID: 44542
I. Burban, “Rational parameterization of algebraic curves,” U sviti Mathematyky, vol. 4, no. 1, 1998.
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1996 | Journal Article | LibreCat-ID: 44544
I. Burban, “Euler’s theorem and map color problems,” U sviti Mathematyky, vol. 2, no. 2, 1996.
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1996 | Journal Article | LibreCat-ID: 44543
I. Burban, “Solutions of equations in integers,” U sviti Mathematyky, vol. 2, no. 4, 1996.
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