Research group Algebra
Welcome to the homepage of the research group "Algebra"
Research
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
Teaching
Lehre im SS 2024:
- Homologische Algebra und Garbentheorie
- Oberseminar "Algebra und Algebraische Geometrie"
- Seminar "Poisson Geometry and Integrable Systems
Lehre im WS 2023/24:
- Einführung in die Darstellungstheorie
- Lineare Algebra I
- Oberseminar "Algebra und Algebraische Geometrie"
- Seminar "Poisson Geometry and Integrable Systems"
Information about teaching in previous semesters can be found on this website.
Publications
Recent Preprints
On the derived categories of gentle and skew-gentle algebras: homological algebra and matrix problems
I. Burban, Yu. Drozd, (2017).
A classification of polyharmonic Maa forms via quiver representations
I. Burban, C. Alfes-Neumann, M. Raum, (2022).
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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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