2005/04/12 by Khazret S. Nirov, Kh. S. Nirov, A. V. Razumov · 8 citations
Mathematics · Physics and Astronomy · #Adjoint representation of a Lie algebra #Advanced Topics in Algebra #Affine Lie algebra #Algebra over a field #Algebraic structures and combinatorial models #Current algebra #Graded Lie algebra #Homotopy and Cohomology in Algebraic Topology #Killing form #Lie algebra #Lie conformal algebra #Mathematics #Pure mathematics #Simple Lie group #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1007/s00220-006-0068-3
published in Communications in Mathematical Physics 267(3), 587-610 (Springer Science+Business Media) · 26 pages
arxiv created 2005/04/12 · openalex publication_date 2006/08/14 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.