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

Details On Z-gradations of twisted loop Lie algebras of complex simple Lie algebras On Z-gradations of twisted loop Lie algebras of complex simple Lie algebras

2005-04-12

arxiv.org/abs/math-ph/0504038v1

Commun.Math.Phys. 267 (2006) 587-610

Physics

Mathematical Physics

26 pages

Scientific paper

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

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