## Lie algebras graded by finite root systems.

**Bruce Allison**

(U. of Alberta)

Abstract: Lie algebras graded by a finite reduced root systems were
introduced in 1992 by S. Berman and R.V. Moody. Since that time the structure
of such Lie algebras has been determined up to central extension in terms
of coordinate algebras. We will describe how to determine the central extensions
of a root graded Lie algebra in terms of the homology of its coordinate
algebra.