On Levi factors of derivation algebras and the radical embedding problem

Francis James Flanigan

Vol. 57 (1975), No. 2, 371–378

DOI: 10.2140/pjm.1975.57.371

Abstract

Problem: given a finite-dimensional nilpotent associative k-algebra N, find all unital associative k-algebras A such that rad A = N. An approach: which subalgebras of Der_kN are images of Lie homomorphisms A∕N → Der_kN? Here the author constructs N over very general fields k such that the “Levi factor” of Der_kN 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_kN.

Mathematical Subject Classification

Primary: 16A72

Milestones

Received: 18 June 1974

Published: 1 April 1975