Research group Algebra

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Research

Research Interests:

  • Homological algebra, derived and triangulated categories
  • Vector bundles and coherent sheaves on singular curves
  • Ringel-Hall algebras and quantum affine algebras
  • Representation theory of associative algebras
  • Fourier-Mukai transforms
  • Cohen-Macaulay modules
  • Yang-Baxter equations

Publications

Published articles

Morita theory for non-commutative noetherian schemes
I. Burban, Yu. Drozd, Advances in Mathematics 399 (2022).
On elliptic solutions of the associative Yang-Baxter equation
I. Burban, A. Peruzzi, Journal of Geometry and Physics 176 (2022).
Algebraic geometry of Lie bialgebras defined by solutions of the classical Yang-Baxter equation
I. Burban, R. Abedin, Communications in Mathematical Physics 387 (2021) 1051–1109.
Cohen-Macaulay modules over the algebra of planar quasi-invariants and Calogero-Moser systems
I. Burban, A. Zheglov, Proceedings of the London Mathematical Society 121 (2020) 1033–1082.
Torsion free sheaves on Weierstraß cubic curves and the classical Yang-Baxter equation
I. Burban, L. Galinat, Communications in Mathematical Physics 364 (2018) 123–169.
Fourier-Mukai transform on Weierstraß cubics and commuting differential operators
I. Burban, A. Zheglov, International Journal of Mathematics 29 (2018).
Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems
I. Burban, Yu. Drozd, Maximal Cohen-Macaulay Modules over Non-Isolated Surface Singularities and Matrix Problems, 1178th ed., 2017.
Simple vector bundles on a nodal Weierstraß cubic and quasi-trigonometric solutions of CYBE
I. Burban, L. Galinat, Journal of Physics A: Mathematical and Theoretical 50 (2017).
Minors of non-commutative schemes
I. Burban, Yu. Drozd, V. Gavran, European Journal of Mathematics 3 (2017) 311–341.
Singular curves and quasi–hereditary algebras
I. Burban, Yu. Drozd, V. Gavran, International Mathematics Research Notices 2017 (2017) 895–920.
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Team

Prof. Dr. Igor Burban

Algebra

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Birgit Duddeck-Buijs

Algebra

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PD Dr. Hans Franzen

Algebra

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Dr. Wassilij Gnedin

Algebra

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Doktor Kyungmin Rho

Algebra

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PhD Stepan Maximov

Algebra

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Dr. Charlene Weiß

Diskrete Mathematik

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Lukas-André Klawuhn

Diskrete Mathematik

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Daniel Perniok

Algebra

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Charly Schwabe

Algebra

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