Finiteness properties of Kac--Moody groups

• Applicant: Professor Dr. Stefan Witzel
• Subject Area: Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 496757904

Kac-Moody groups generalize two important classes of groups that are of fundamental importance in mathematics and physics: Kac-Moody groups over finite fields generalize finite groups of Lie type, which account for for almost all of the finite simple groups; Kac-Moody groups over the real and complex numbers generalize Lie groups.Contrary to their classical counterparts Kac-Moody groups lack important finiteness properties: Kac-Moody groups over finite fields are infinite in general; Kac-Moody groups over the real and complex numbers are infinite-dimensional in general.The goal of the project is to determine topological finiteness properties of Kac-Moody groups over finite fields. These properties generalize the properties of being finitely generated and of being finitely presented and they are coarse invariants.

• DFG Programme: Research Grants