Triality and Algebraic Groups of Type $^3D_4$
Group Theory
2014-09-08 v1
Abstract
We determine which simple algebraic groups of type 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.
Cite
@article{arxiv.1409.1718,
title = {Triality and Algebraic Groups of Type $^3D_4$},
author = {Max-Albert Knus and Jean-Pierre Tignol},
journal= {arXiv preprint arXiv:1409.1718},
year = {2014}
}