Some twisted variants of Chevalley groups. (English) Zbl 1137.20042

Steinbach, Anja

Bull. Belg. Math. Soc. - Simon Stevin 12, No. 4, 491-503 (2005).

Summary: We construct a BN-pair for subgroups of Chevalley groups, which are fixed under some distinguished automorphisms. This generalizes the standard approach for the twisted groups of type \(^2A_\ell\), \(^2D_\ell\) and \(^2E_6\) to groups which are not necessarily quasi-split.

MSC:

20G15	Linear algebraic groups over arbitrary fields
20E42	Groups with a \(BN\)-pair; buildings
20F55	Reflection and Coxeter groups (group-theoretic aspects)
20E07	Subgroup theorems; subgroup growth

Keywords:

Chevalley groups; Steinberg variation; BN-pairs; root systems