Arbeitsgruppe Algebra

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For­schung

Aktuelle Forschungsprojekte:

  • Homologische Algebra, abgeleitete und triangulierte Kategorien
  • Vektorbündel und kohärente Garben auf singulären Kurven
  • Ringel-Hall-Algebren und quanten affinen Algebren
  • Darstellungstheorie der assoziativen Algebren
  • Fourier-Mukai-Transformationen
  • Cohen-Macaulay-Moduln
  • Yang-Baxter-Gleichungen

Publikationen

Ver­öf­fent­li­chun­gen

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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Ak­ti­vi­tä­ten

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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