Vol. 57, No. 2, 1975

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On Levi factors of derivation algebras and the radical embedding problem

Francis James Flanigan

Vol. 57 (1975), No. 2, 371–378

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 DerkN are images of Lie homomorphisms A∕N DerkN? Here the author constructs N over very general fields k such that the “Levi factor” of DerkN 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 An,Bn,Cn,Dn is Levi factor of some DerkN.

Mathematical Subject Classification
Primary: 16A72
Received: 18 June 1974
Published: 1 April 1975
Francis James Flanigan