Skip Garibaldi: Outer automorphisms of algebraic groups and determining groups by their maximal tori

Submission: 2010, May 22 (revised 2011, Feb 4, former title: Weak commensurability and forms of Spin_4n)

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 D2n 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.

2000 Mathematics Subject Classification: Primary 20G30; Secondary 11E72, 20G15.

Keywords and Phrases: weak commensurability, triality, outer automorphisms

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