The Jordan socle and finitary Lie algebras
In this paper we introduce the notion of
Jordan socle for nondegenerate Lie algebras, which extends the
definition of socle for 3-graded Lie algebras. Any nondegenerate Lie
algebra with
essential Jordan socle is an essential subdirect product of strongly
prime ones having nonzero Jordan socle.
These last algebras are described, up to exceptional cases, in terms of
simple finitary Lie
algebras and their algebras of derivations. When working with Lie
algebras which are infinite dimensional over
an algebraically closed field of characteristic zero, the
exceptions disappear and the algebras of
derivations are computed.
(This paper has appeared in J. Algebra
280 (2004), 635--654)
A. Fernández López < emalfer@agt.cie.uma.es >
E. García < egarciag@mat.ucm.es >
M. Gómez Lozano < magomez@agt.cie.uma.es >