On mathbb{Z}-Gradations of Twisted Loop Lie Algebras of Complex Simple Lie Algebras |
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Authors: | Kh. S. Nirov A. V. Razumov |
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Affiliation: | (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 |
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Abstract: | We define the twisted loop Lie algebra of a finite dimensional Lie algebra as the Fréchet space of all twisted periodic smooth mappings from to. Here the Lie algebra operation is continuous. We call such Lie algebras Fréchet Lie algebras. We introduce the notion of an integrable-gradation of a Fréchet Lie algebra, and find all inequivalent integrable-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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