(24). A construction of gradings of Lie Algebras

Autores: A. Fernández López, E. García, M. Gómez Lozano y E. Neher. (JCR:53 de 207. Factor de impacto 0.722)

Revista: International Mathematical Research Notices. (2007); Vol. 2007 : article ID rnm051, 34 pages, doi:10.1093/imrn/rnm051.

Abstract:In this paper we present a method to construct gradings of Lie algebras. It requires the existence of an abelian inner ideal $B$ of the Lie algebra whose subquotient, a Jordan pair, is covered by a finite grid, and it produces a grading of the Lie algebra $L$ by the weight lattice of the root system associated to the covering grid. As a corollary one obtains a finite $\ZZ$-grading $L=L_{-n} \oplus \cdots \oplus L_n$ such that $B=L_n$. In particular, our assumption on $B$ holds for abelian inner ideals of finite length in nondegenerate Lie algebras.