ON THE STRUCTURE OF SYMMETRICAL SELF-DUAL LIE-ALGEBRAS

A finite-dimensional Lie algebra is called (symmetric) self-dual, if i t possesses an invariant nondegenerate (symmetric) bilinear form. Symm etric self-dual Lie algebras have been studied by Medina and Revoy, wh o have proven a very useful theorem about their structure, In this pap er we prove a refinement of their theorem that has wide applicability in conformal field theory, where symmetric self-dual Lie algebras star t to play an important role due to the fact that they are precisely th e Lie algebras that admit a Sugawara construction, We also prove a few corollaries that are important in conformal field theory. (C) 1996 Am erican Institute of Physics.