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

Kh. S. Nirov·A. V. Razumov
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Abstract

We define the twisted loop Lie algebra of a finite dimensional Lie algebra $\mathfrak g$ as the Fréchet 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 Fréchet Lie algebras. We introduce the notion of an integrable $\mathbb Z$-gradation of a Fréchet 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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Kh. S. Nirov, A. V. Razumov. 2005-04-12. On Z-gradations of twisted loop Lie algebras of complex simple Lie algebras. https://doi.org/10.1007/s00220-006-0068-3

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