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Algebra
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Publications

Recent preprints

  • C.Alfes-Neumann, I.Burban, M.Raum, A classification of polyramonic Maaß forms via quiver representations (pdf), arXiv:2207.02278
  • I.Burban, Yu.Drozd, Non-commutative nodal curves and derived tame algebras (pdf), arXiv:1805.05174.
  • I.Burban, Yu.Drozd, On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems (pdf), arXiv:1706.08358.

Recent publications

  • I. Burban, A.Peruzzi, On elliptic solutions of the associative Yang-Baxter equation (pdf), J.Geom.Phys. 176 (2022), no.104499, 10 pp.
  • I.Burban, Yu.Drozd, Morita theory for non-commutative noetherian schemes (pdf), Adv. Math. 399 (2022), no. 108273, 42 pp.
  • R.Abedin, I. Burban, Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation (pdf), Comm. Math. Phys. 387 (2021), no. 2, 1051–1109.
  • I.Burban, A.Zheglov, Cohen-Macaulay modules over the algebra of planar quasi-invariants and Calogero-Moser systems (pdf), Proc. Lond. Math. Soc. (3) 121 (2020), no. 4, 1033–1082
  • I.Burban, L.Galinat, Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter equation (pdf), Comm. Math. Phys. 364 (2018), no. 1,  123–169.
  • I.Burban, A.Zheglov, Fourier-Mukai transform on Weierstraß cubics and commuting differential operators (pdf), Internat. J. Math. 29 (2018), no. 10, 1850064, 46 pp.
  • I.Burban, L.Galinat, A.Stolin, Simple vector bundles on a nodal Weierstraß cubic and quasi-trigonometric solutions of CYBE (pdf), Journal of Physics A 50 (2017), no. 45,  454002.
  • I.Burban, Yu.Drozd, Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems (pdf), Memoirs of the AMS, vol. 248, no. 1178 (2017).
  • I.Burban, Yu.Drozd, V.Gavran, Minors of non-commutative schemes (pdf), European Journal of Math. 3 (2017), no. 2, 311-341.
  • I.Burban, Yu.Drozd, V.Gavran, Singular curves and quasi-hereditary algebras (pdf), Int. Math. Res. Notices, vol. 2017, no. 3, 895-920 (2017).
  • I.Burban, W.Gnedin, Cohen-Macaulay modules over some non-reduced curve singularities (pdf), Journal of Pure and Applied Algebra, vol. 220, no. 12, 3777-3815 (2016).
  • I.Burban, T.Henrich, Vector bundles on plane cubic curves and the classical Yang-Baxter equation (pdf), Journal of the European Math. Society, vol. 17, no. 3, 591-644 (2015).
  • I.Burban, B.Kreussler, Analytic moduli spaces of simple sheaves on families of integral curves (pdf), Math. Nachr., vol. 287, no. 2-3, 173-183 (2014).
  • I.Burban, O.Schiffmann, Composition algebra of a weighted projective line (pdf), Journal für Reine und Angew. Mathematik, vol. 679, 75-124 (2013).
  • I.Burban, M.Kalck, Relative singularity category of a non-commutative resolution of singularities (pdf), Adv. in Math., vol. 231, no. 1, 414-435 (2012).
  • I.Burban, Frobenius morphism and vector bundles on cycles of projective lines (pdf), Comm. in Algebra, vol. 40, no. 8, 2983-2988 (2012).
  • I.Burban, T.Henrich, Semi-stable vector bundles on elliptic curves and the associative Yang-Baxter equation (pdf), Journal of Geometry and Physics, vol. 62, no. 2, 312-329 (2012).
  • I.Burban, B.Kreussler, Vector bundles on degenerations of elliptic curves and Yang-Baxter equations (pdf), Memoirs of the AMS, vol. 220, no. 1035 (2012).
  • I.Burban, O.Schiffmann, Two descriptions of the quantum affine algebra $U_v(sl^_2)$ via Hall algebra approach (pdf), Glasgow Mathematical Journal, vol. 54, no. 2, 283-307 (2012).
  • I.Burban, O.Schiffmann, On the Hall algebra of an elliptic curve I (pdf), Duke Math. Journal, vol. 161, no. 7, 1171-1231 (2012).
  • I.Burban, Yu.Drozd, Tilting on non-commutative rational projective curves (pdf), Mathematische Annalen, vol. 351, no. 3, 665-709 (2011).

Lecture Notes

  • Du Val Singularities (pdf)
  • Coherent sheaves on an elliptic curve (pdf), Notes of Kristian Bruening of my lecture course given at Tsinghua University in August 2005, Beijing, China.
  • Maximal Cohen-Macaulay modules over quotient surface singularities (pdf). These are notes of my talks given in Paderborn and Osaka in 2009.
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