On \mathbb{Z}-Gradations of Twisted Loop Lie Algebras of Complex Simple Lie Algebras期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On \mathbb{Z}-Gradations of Twisted Loop Lie Algebras of Complex Simple Lie Algebras

Authors:	Kh S Nirov A V Razumov

Institution:	(1) Max-Planck-Institut für Gravitationsphysik – Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Golm b. Potsdam, Germany;(2) Institute for High Energy Physics, 142281 Protvino Moscow Region, Russia

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.On leave of absence from the Institute for Nuclear Research of the Russian Academy of Sciences, 117312 Moscow, Russia.

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