On the structure of symmetric self-dual Lie algebras

Details On the structure of symmetric self-dual Lie algebras On the structure of symmetric self-dual Lie algebras

1995-06-22

arxiv.org/abs/hep-th/9506152v2

J.Math.Phys. 37 (1996) 4121-4134

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, .dvi.uu (needs AMSFonts 2.1+)

Scientific paper

10.1063/1.531620

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 which 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 which admit a Sugawara construction. We also prove a few corollaries which are important in Conformal Field Theory. (This paper provides mathematical details of results used, but only sketched, in the companion paper hep-th/9506151.)

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