On Z-gradations of twisted loop lie algebras of complex simple lie algebras

摘要

We define the twisted loop Lie algebra of a finite dimensional Lie algebra g as the Frechet space of all twisted periodic smooth mappings from R to g. Here the Lie algebra operation is continuous. We call such Lie algebras Frechet Lie algebras. We introduce the notion of an integrable Z-gradation of a Frechet Lie algebra, and find all inequivalent integrable Z-gradations with finite dimensional grading subspaces of twisted loop Lie algebras of complex simple Lie algebras.