1995/06/23 by JM Figueroa-O'Farrill, José M. Figueroa-O’Farrill, Sonia Stanciu +1 · 5 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #hep-th
paper · pdf · doi:10.1063/1.531620
published as J.Math.Phys. 37 (1996) 4121-4134 · 19 pages, .dvi.uu (needs AMSFonts 2.1+)
arxiv created 1995/06/23 · openalex publication_date 1996/08/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A finite-dimensional Lie algebra is called (symmetric) self-dual, if it possesses an invariant nondegenerate (symmetric) bilinear form. Symmetric self-dual Lie algebras have been studied by Medina and Revoy, who have proven a very useful theorem about their structure. In this paper we prove a refinement of their theorem that has wide applicability in conformal field theory, where symmetric self-dual Lie algebras start to play an important role due to the fact that they are precisely the Lie algebras that admit a Sugawara construction. We also prove a few corollaries that are important in conformal field theory.