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Communications in Mathematical Physics

, Volume 267, Issue 3, pp 587–610 | Cite as

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

  • Kh. S. NirovEmail author
  • A. V. Razumov
Article

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.

Keywords

Topological Vector Space Dimensional Manifold Loop Group Continuous Linear Mapping Grade Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Max-Planck-Institut für Gravitationsphysik – Albert-Einstein-InstitutGolm b. PotsdamGermany
  2. 2.Institute for High Energy PhysicsProtvino Moscow RegionRussia

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