(14). The Jordan Socle and Finitary Lie algebra.

Autores: A. Fernández López, E. García, y M. Gómez Lozano.  

Revista: J. Algebra. 280(2), (2004) 635–654. (JCR: 57 de 180. Factor de impacto 0.554)

Abstract: In this paper we introduce the notion of Jordan socle for nondegenerate Lie algebras, which extends the definition of socle given in [11] 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.