Okubo algebras in characteristic 3 and their automorphisms

Authors
Citation
A. Elduque, Okubo algebras in characteristic 3 and their automorphisms, COMM ALGEB, 27(6), 1999, pp. 3009-3030
Citations number
21
Categorie Soggetti
Mathematics
Journal title
COMMUNICATIONS IN ALGEBRA
ISSN journal
00927872 → ACNP
Volume
27
Issue
6
Year of publication
1999
Pages
3009 - 3030
Database
ISI
SICI code
0092-7872(1999)27:6<3009:OAIC3A>2.0.ZU;2-1
Abstract
Associated to any eight-dimensional non-unital composition algebra with ass ociative norm, there are outer automorphisms of order 3 of the correspondin g spin group, such that the fixed subgroup is the automorphism group of the composition algebra, Over fields of characteristic not equal 3 these are s imple algebraic groups of types G(2) or A(2), related respectively to the p ara-octonion and the Okubo algebras. A connection between the Okubo algebras over fields of characteristic 3 wit h some simple noncommutative Jordan algebras will be used to compute explic itly the automorphism groups and Lie algebras of derivations of these algeb ras. In contrast to the other characteristics, the groups will no longer be of type A(2) and will either be trivial or contain a large unipotent radic al.