On automorphisms of Lie algebras of classical type. II

Abstract

ceptional Jordan algebra a. Except for fields of characteristic 2 and 3, the interpretations of these Lie algebras given for characteristic zero by Chevalley and Schafer [3 ] are shown to carry over to arbitrary base fields. When several more low characteristics are exempted from consideration (on the basis of a failure of applicability of certain results on exponentials in [10]), the structure of the automorphism groups of these algebras is here determined in terms of certain linear groups acting in a. Some of the latter groups have also been studied recently by Jacobson [6; 7], who has proved the simplicity of a group here shown to be isomorphic to the group of invariant automorphisms of the Lie algebra in question (F4 or E6). The present paper also demonstrates the simplicity of these groups, by showing that they can be identified with groups whose simplicity has been proved by Chevalley [2]. 1. Derivations of the split exceptional Jordan algebra. Let (? be the split Cayley algebra over a field j of characteristic F 2, regarded as all matrices of the form ta\