The isomorphism problem for almost split Kac-Moody groups

Abstract

We consider the isomorphism problem for almost split Kac--Moody groups, which have been constructed by Rémy via Galois descent from split Kac-Moody groups as defined by Tits. We show that under certain technical assumptions, any isomorphism between two such groups must preserve the canonical subgroup structure, i.e. the twin root datum associated to these groups, which generalizes results of Caprace in the split case. An important technical tool we use is the existence of maximal split subgroups inside almost split Kac-Moody groups, which generalizes the corresponding result of Borel-Tits for reductive algebraic groups.

29 pages, based on a part of the author's Ph.D. thesis

References in corpus (1)

• Finiteness Properties of Chevalley Groups over a Polynomial Ring over a Finite Field

Cited by in corpus (2)

• A fixed point theorem for Lie groups acting on buildings and applications to Kac-Moody theory
• Embeddings of algebraic groups in Kac-Moody groups