(35). Principal Filtrations of Lie algebras.

Autores: E. García and M. Gómez Lozano  

Revista:Communications in Algebra. (40) (2012),: 3622–3628.       (JCR: 246 de 296 Factor de impacto: 0.356)

Abstract:We show that any ad-nilpotent element $x$ of index less than or equal to three of a Lie algebra $L$ defines a 5-filtration in $L$. When $L$ is nondegenerate, the $\mathbb{Z}$-graded Lie algebra $\hat L$ associated to this filtration is isomorphic to $L$ if and only $x$ is von Neumann regular, if and only if $\hat L$ is nondegenerate.