Tits indices over semilocal rings
Algebraic Geometry
2010-01-15 v3 Group Theory
Abstract
We give a simplified proof of Tits' classification of semisimple algebraic groups that remains valid over semilocal rings. In particular, we provide explicit necessary and sufficient conditions that anisotropic groups of a given type appear as anisotropic kernels of semisimple groups of a given Tits index. We also give a new proof of the existence of all indices of exceptional inner type using the notion of canonical dimension of projective homogeneous varieties.
Cite
@article{arxiv.0807.2140,
title = {Tits indices over semilocal rings},
author = {V. Petrov and A. Stavrova},
journal= {arXiv preprint arXiv:0807.2140},
year = {2010}
}
Comments
an existence proof added; 29 pages