(27). An Artinian theory for Lie algebras

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

Revista: J. Algebra. 319 (2008) 938–951 (JCR: 89 de 214. Factor de impacto: 0.668)

Abstract: 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.