Complemented Lie algebras are introduced in this paper (a notion similar to that studied by O. Loos and E. Neher in Jordan pairs). We prove that a Lie algebra is complemented if and only if it is a direct sum of simple nondegenerate Artinian Lie algebras.
Moreover, we classify simple nondegenerate Artinian Lie algebras over a field of characteristic 0 or greater than 7, and describe the Lie inner ideal structure of simple Lie algebras arising from simple associative algebras with nonzero socle.
(This paper has appeared in J. Algebra 319 (2008), 938--951)
A. Fernández < emalfer@agt.cie.uma.es >
E. García < esther.garcia@urjc.es >
M. Gómez Lozano < magomez@agt.cie.uma.es >