Affine Kac–Moody groups: analysis, algebra, and arithmetic (A05)

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

Affine Kac-Moody groups and related groups (like loop groups) will be studied from several perspectives. We shall investigate finiteness properties of special linear groups over Laurent polynomials over the ring of integers. We also strive to classify certain maximal Lie orders corresponding to trigonometric solutions of the classical Yang-Baxter equation. In both cases, group actions on affine twin buildings are an essential tool. Such solutions give rise to Lie-Poisson structures on loop groups. The requisite theory of infinite-dimensional Lie-Poisson groups and related Poisson geometry will be developed.

• DFG Programme: CRC/Transregios
• Subproject of: TRR 358: Integral Structures in Geometry and Representation Theory
• Applicant Institution: Universität Bielefeld
• Project Heads: Professor Dr. Igor Burban; Professor Dr. Kai-Uwe Bux; Professor Dr. Helge Glöckner