Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9493578 | Journal of Algebra | 2005 | 36 Pages |
Abstract
A Jordan algebra J over a field k of characteristic 2 becomes a 2-Lie algebra L(J) with Lie product [x,y]=xây and squaring x[2]=x2. We determine the precise ideal structure of L(J) in case J is simple finite-dimensional and k is algebraically closed. We also decide which of these algebras have smooth automorphism groups. Finally, we study the derivation algebra of a reduced Albert algebra J=H3(O,k) and show that DerJ has a unique proper nonzero ideal VJ, isomorphic to L(J)/kâ
1J, with quotient DerJ/VJ independent of O. On the group level, this gives rise to a special isogeny between the automorphism group of J and that of the split Albert algebra, whose kernel is the infinitesimal group determined by VJ.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Pablo Alberca Bjerregaard, Ottmar Loos, Cándido MartÃn González,