Submission: 2008, Jul 16
We present a simplified version of Tits' proof of the classification of semisimple algebraic groups, which remains valid over semilocal rings. We also provide explicit conditions on anisotropic groups to appear as anisotropic kernels of semisimple groups of a given index.
2000 Mathematics Subject Classification: 20G15; 20G35
Keywords and Phrases: semisimple algebraic groups; Tits index; Tits algebras
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