Outer automorphisms of algebraic groups and determining groups by their maximal tori

Details Outer automorphisms of algebraic groups and determining groups by their maximal tori Outer automorphisms of algebraic groups and determining groups by their maximal tori

2010-06-07

arxiv.org/abs/1006.1298v3

Mathematics

Group Theory

v2: Small changes and new title since v1 // v3: Expanded the introduction

Scientific paper

We give a cohomological criterion for existence of outer automorphisms of a semisimple algebraic group over an arbitrary field. This criterion is then applied to the special case of groups of type D_2n over a global field, which completes some of the main results from the paper "Weakly commensurable arithmetic groups and isospectral locally symmetric spaces" (Pub. Math. IHES, 2009) by Prasad and Rapinchuk and gives a new proof of a result from another paper by the same authors.

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