Derivations and automorphisms of Jordan algebras in characteristic two

AbstractA Jordan algebra J over a field k of characteristic 2 becomes a 2-Lie algebra L(J) with Lie product [x,y]=x○y 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)/k⋅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