Automorphism groups of simple Kokoris algebras

Abstract

The structure of the automorphism groups of certain classes of simple Kokoris algebras is studied in this paper. A solvable locally nilpotent normal subgroup of the automorphism group of an arbitrary Kokoris algebra is described, the factors of its normal series being elementary abelian p-groups. Connections between automorphisms and derivations for two particular classes of algebras, those defined by skew-symmetric bilinear forms and those of dimension p 2, are detailed. These connections then make it possible to count the number of components of a direct sum decomposition of the normal series factors in terms of the dimensions of specified subspaces of associated Lie algebras of derivations.