The isomorphism problem for almost split Kac-Moody groups

Details The isomorphism problem for almost split Kac-Moody groups The isomorphism problem for almost split Kac-Moody groups

2011-09-05

arxiv.org/abs/1109.0906v1

Mathematics

Group Theory

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

Scientific paper

We consider the isomorphism problem for almost split Kac--Moody groups, which have been constructed by R\'emy 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.

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