On Levi factors of derivation algebras and the radical embedding problem

Abstract

Problem: given a finite-dimensional nilpotent associative fc-algebra N, find all unital associative A>algebras A such that rad A -N. An approach: which subalgebras of Der* N are images of Lie homomorphisms A/N-^er k N Here the author constructs N over very general fields k such that the "Levi factor" of er k N is a direct sum of orthogonal Lie algebras o(V, b) of arbitrarily prescribed symmetric and alternate bilinear spaces. In particular, if k is algebraically closed of characteristic zero, then every direct sum of classical simple Lie algebras A n , B n , C n , D n is Levi factor of some Der fc JN.