Tits indices over semilocal rings

2008/07/14 by V. Petrov, Petrov, V., A. Stavrova +1 · 2 citations
Mathematics · #20G15 #20G35 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.GR #msc:20G15 #msc:20G35

paper · pdf · doi:10.48550/arxiv.0807.2140

an existence proof added; 29 pages

arxiv created 2010/01/15 · arxiv updated 2010/02/08

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.

Cited by

• Locally isotropic Steinberg groups II. Schur multipliers
• Abstract isomorphisms of isotropic root graded groups over rings

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