On the structure of symmetric self-dual Lie algebras
Abstract
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.)
Keywords
Cite
@article{arxiv.hep-th/9506152,
title = {On the structure of symmetric self-dual Lie algebras},
author = {JM Figueroa-O'Farrill and S Stanciu},
journal= {arXiv preprint arXiv:hep-th/9506152},
year = {2009}
}
Comments
19 pages, .dvi.uu (needs AMSFonts 2.1+)