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45 Publications
2022 | Journal Article | LibreCat-ID: 44328
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
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| DOI
2022 | Preprint | LibreCat-ID: 44537
Burban, I., Alfes-Neumann, C., & Raum, M. (2022). A classification of polyharmonic Maa forms via quiver representations.
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2022 | Journal Article | LibreCat-ID: 44327
Burban, I., & Peruzzi, A. (2022). On elliptic solutions of the associative Yang-Baxter equation. Journal of Geometry and Physics, 176, Article 104499.
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2021 | Journal Article | LibreCat-ID: 44329
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
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| DOI
2020 | Journal Article | LibreCat-ID: 44331
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
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| DOI
2018 | Journal Article | LibreCat-ID: 44333
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
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| DOI
2018 | Preprint | LibreCat-ID: 44538
Burban, I., & Drozd, Yu. (2018). Non-commutative nodal curves and derived tame algebras.
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2018 | Journal Article | LibreCat-ID: 44332
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.
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2017 | Book | LibreCat-ID: 44337
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
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| DOI
2017 | Preprint | LibreCat-ID: 44539
Burban, I., & Drozd, Yu. (2017). On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems.
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2017 | Journal Article | LibreCat-ID: 44334
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.
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2017 | Journal Article | LibreCat-ID: 44335
Burban, I., Drozd, Yu., & Gavran, V. (2017). Minors of non-commutative schemes. European Journal of Mathematics, 3(2), 311–341.
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2017 | Journal Article | LibreCat-ID: 44336
Burban, I., Drozd, Yu., & Gavran, V. (2017). Singular curves and quasi–hereditary algebras. International Mathematics Research Notices 2017, 3, 895–920.
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2016 | Journal Article | LibreCat-ID: 44339
Burban, I., & Gnedin, W. (2016). Cohen-Macaulay modules over some non-reduced curve singularities. Journal of Pure and Applied Algebra, 220(12), 3777–3815.
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2015 | Journal Article | LibreCat-ID: 44340
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
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| DOI
2014 | Journal Article | LibreCat-ID: 44341
Burban, I., & Kreußler, B. (2014). Analytic moduli spaces of simple sheaves on families of integral curves. Mathematische Nachrichten, 287(2–3), 173–183.
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2013 | Journal Article | LibreCat-ID: 44342
Burban, I., & Schiffmann, O. (2013). Composition algebra of a weighted projective line. Journal Für Reine Und Angew. Mathematik, 679, 75–124.
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2012 | Book | LibreCat-ID: 44346
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
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| DOI
2012 | Journal Article | LibreCat-ID: 44344
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
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| DOI
2012 | Journal Article | LibreCat-ID: 44345
Burban, I., & Henrich, T. (2012). Semi-stable vector bundles on elliptic curves and the associative Yang-Baxter equation. Journal of Geometry and Physics, 62(2), 312–329.
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2012 | Journal Article | LibreCat-ID: 44347
Burban, I., & Schiffmann, O. (2012). Two descriptions of the quantum affine algebra Uv(sl2) via Hall algebra approach. Glasgow Journal of Math., 54(2), 283–307.
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2012 | Journal Article | LibreCat-ID: 44348
Burban, I. (2012). Frobenius morphism and vector bundles on cycles of projective lines. Communications in Algebra, 40(8), 2983–2988.
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2012 | Journal Article | LibreCat-ID: 44343
Burban, I., & Kalck, M. (2012). Singularity category of a non–commutative resolution of singularities. Advances in Mathematics, 231(1), 414–435.
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2011 | Journal Article | LibreCat-ID: 44349
Burban, I., & Drozd, Yu. (2011). Tilting on non–commutative rational projective curves. Mathematische Annalen, 351(3), 665–709.
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2008 | Journal Article | LibreCat-ID: 44350
Burban, I., Iyama, O., Keller, B., & Reiten, I. (2008). Cluster tilting for one–dimensional hypersurface singularities. Advances in Mathematics, 217(6), 2443–2484. https://doi.org/10.1016/j.aim.2007.10.007
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| DOI
2008 | Book Chapter | LibreCat-ID: 44530
Burban, I., & Drozd, Yu. (2008). Maximal Cohen-Macaulay modules over surface singularities. In Trends in Representations of Algebras and Related Topics (pp. 101–160). EMS Publishing House.
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2006 | Book Chapter | LibreCat-ID: 44531
Burban, I., Bodnarchuk, L., Drozd, Yu., & Greuel, G.-M. (2006). Vector bundles and torsion free sheaves on degenerations of elliptic curves. In Global Aspects of Complex Geometry (pp. 83–129). Springer.
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2006 | Journal Article | LibreCat-ID: 44352
Burban, I., & Kreußler, B. (2006). On a relative Fourier–Mukai transform on genus one fibrations. Manuscripta Mathematica, 120(3), 283–306.
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2006 | Journal Article | LibreCat-ID: 44351
Burban, I., & Kreußler, B. (2006). Derived categories of irreducible projective curves of arithmetic genus one. Compositio Mathematica, 142, 1231–1262.
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2005 | Book Chapter | LibreCat-ID: 44532
Burban, I., & Drozd, Yu. (2005). 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, pp. 23–46).
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2005 | Journal Article | LibreCat-ID: 44354
Burban, I. (2005). Derived Categories and D-Branes. Ukrain. Mat. Zh., 57(1).
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2005 | Journal Article | LibreCat-ID: 44353
Burban, I., & Kreußler, B. (2005). Fourier-Mukai transforms and semi-stable sheaves on nodal Weierstraß cubics. J. Reine Angew. Math., 584, 45–82.
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2004 | Journal Article | LibreCat-ID: 44355
Burban, I., & Drozd, Yu. (2004). Coherent sheaves on rational curves with simple double points and transversal intersections. Duke Mathematical Journal, 121(2), 189–229. https://doi.org/10.1215/S0012-7094-04-12121-9
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| DOI
2004 | Conference Paper | LibreCat-ID: 44533
Burban, I., & Drozd, Yu. (2004). Indecomposables of the derived categories of certain associative algebras. Proceedings of the ICRA-X Conference, Toronto 2002, 45, 109–127.
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2004 | Book Chapter | LibreCat-ID: 44534
Burban, I. (2004). 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, pp. 173–188). American Mathematical Society.
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2004 | Journal Article | LibreCat-ID: 44356
Burban, I., & Drozd, Yu. (2004). Derived tameness of nodal algebras. J. Algebra, 272(1), 46–94.
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2003 | Journal Article | LibreCat-ID: 44357
Burban, I. (2003). Stable vector bundles on a rational curve with one node. Ukrain. Mat. Zh., 55(7), 867–874.
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2002 | Conference Paper | LibreCat-ID: 44535
Burban, I., & Drozd, Yu. (2002). Derived categories and matrix problems. Ukrainian Mathematical Congress 2001. Algebraic Structures and Their Applications. Proceedings of the Third International Algebraic Conference Held in Framework of the Ukrainian Mathematical Congress, 201–211.
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2002 | Journal Article | LibreCat-ID: 44358
Burban, I., & Freiermuth, H.-G. (2002). Geometrical properties of sections of Buchsbaum- Rim sheaves. Le Matematiche, LVII, 265–283.
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2001 | Book Chapter | LibreCat-ID: 44536
Burban, I., Drozd, Yu., & Greuel, G.-M. (2001). Vector bundles on singular projective curves. In C. Ciliberto (Ed.), Applications of algebraic geometry to coding theory, physics and computation (pp. 1–15). Kluwer Academic Publishers.
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1998 | Journal Article | LibreCat-ID: 44541
Burban, I., & Duma, W. (1998). Projective transformations of a plane. U Sviti Mathematyky, 4(2).
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1998 | Journal Article | LibreCat-ID: 44540
Burban, I., & Duma, W. (1998). Projective transformations of a plane and three-dimensional space. U Sviti Mathematyky, 4(4).
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1998 | Journal Article | LibreCat-ID: 44542
Burban, I. (1998). Rational parameterization of algebraic curves. U Sviti Mathematyky, 4(1).
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1996 | Journal Article | LibreCat-ID: 44544
Burban, I. (1996). Euler’s theorem and map color problems. U Sviti Mathematyky, 2(2).
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1996 | Journal Article | LibreCat-ID: 44543
Burban, I. (1996). Solutions of equations in integers. U Sviti Mathematyky, 2(4).
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