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 >