Hereditary categories, reflection groups, and non-commutative curves (C02)

• Subject Area: Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 491392403

There are deep connections between quiver representations and Coxeter groups involving the associated root systems, Lie algebras and quantum groups. We will study a parallel situation in which coherent sheaves on certain non-commutative curves, called exceptional curves, correspond to other types of reflection groups. Such exceptional curves include weighted projective lines, but when the base field is not algebraically closed, there are other examples which we want to concentrate on. We will also study the associated non-crossing partitions and Artin groups.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 358: Integral Structures in Geometry and Representation Theory
• Applicant Institution: Universität Bielefeld
• Project Heads: Privatdozentin Dr. Barbara Baumeister; Professor Dr. Igor Burban; Professor Dr. William Crawley-Boevey