Triality and Algebraic Groups of Type ³D₄

2014/09/05 by Knus, Max-Albert, Tignol, Jean-Pierre
#11E72 #17A75 #20G15 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1409.1718

Abstract

We determine which simple algebraic groups of type ³D₄ over arbitrary fields of characteristic different from 2 admit outer automorphisms of order 3, and classify these automorphisms up to conjugation. The criterion is formulated in terms of a representation of the group by automorphisms of a trialitarian algebra: outer automorphisms of order 3 exist if and only if the algebra is the endomorphism algebra of an induced cyclic composition; their conjugacy classes are in one-to-one correspondence with isomorphism classes of symmetric compositions from which the induced cyclic composition stems.

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• Outer automorphisms of classical algebraic groups
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