Derivations and automorphisms of Jordan algebras in characteristic two
A Jordan algebra J over a field k of characteristic 2 becomes a
restricted Lie algebra L(J) with Lie product given by the circle product and squaring
operation the usual square in J. 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 case where J is a reduced Albert algebra (3 by 3 hermitian
matrices over a Cayley algebra over k with diagonal coefficients in k) and
show that Der(J) has a unique proper nonzero ideal V_J, isomorphic to
L(J)/k.1, with quotient Der(J)/V_J independent of the Cayley algebra. 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 V_J.
(Corrected version 26 Oct 2004, to appear in J. Algebra)
P. Alberca < p_alberca@ctima.uma.es >
O. Loos < ottmar.loos@uibk.ac.at >
C. Martín < candido_martin_gonzalez@hotmail.com >