On Levi factors of derivation algebras and the radical embedding problem
Francis J. Flanigan · Pacific Journal of Mathematics · 1975
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-^Ώer k NΊ Here the author constructs N over very general fields k such that the "Levi factor" of Όer 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 JNΓ.l Some questions* We ask initially: What are the possible