A construction of gradings of Lie algebras

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 ring. As a corollary one obtains a finite Z-grading L=Ln+...+L1+L0+L-1 +...+L-n such  that B=Ln. In particular, our assumption on B holds for abelian inner ideals of finite length in nondegenerate Lie algebras.

(This is an extendend version of paper number 213)

(This paper has appeared in Int. Math. Res. Notices 2007, no. 16, Art. ID rnm051, 34 pp)

A. Fernández López < emalfer@agt.cie.uma.es >

E. García < esther.garcia@urjc.es >

M. Gómez Lozano < magomez@agt.cie.uma.es >

E. Neher < neher@uottawa.ca >

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