Kac-Moody groups: split and relative theories. Lattices

Details Kac-Moody groups: split and relative theories. Lattices Kac-Moody groups: split and relative theories. Lattices

2002-11-17

arxiv.org/abs/math/0211258v1

Mathematics

Group Theory

45 pages, 9 figures

Scientific paper

In this survey article, we recall some facts about split Kac-Moody groups as defined by J. Tits, describe their main properties and then propose an analogue of Borel-Tits theory for a non-split version of them. The main result is a Galois descent theorem, i.e. the persistence of a nice combinatorial structure after passing to rational points. We are also interested in the geometric point of view, namely the production of new buildings admitting (nonuniform) lattices.

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