Kac-moody Groups: Split and Relative Theories. Lattices
نویسنده
چکیده
— 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.
منابع مشابه
Lattices in Kac - Moody Groups
Initially, we set out to construct non-uniform ‘arithmetic’ lattices in Kac-Moody groups of rank 2 over finite fields, as constructed by Tits ([Ti1], [Ti2]) using the BruhatTits tree of a Tits system for such groups. This attempt succeeded, and in fact, the construction we used can be applied to higher rank Kac-Moody groups over sufficiently large finite fields, and their buildings (Theorem 1.7...
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