Central extensions of Lie algebras graded by finite root systems

Lie algebras graded by finite irreducible reduced root systems have been classified up to central extensions by Berman and Moody, Benkart and Zelmanov, and Neher. In this paper we determine the central extensions of these Lie algebras and hence describe them completely up to isomorphism. The center of the universal covering algebra of such a Lie algebra L is shown to be isomorphic to a certain homology group of the coordinate algebra of L. This coordinate algebra is either associative, alternative, Jordan or the Pierce one-half space of a Jordan algebra, according to the type of L.

(This paper has appeared in Math.Ann. 316 (2000), 499-527)

B.N. Allison <bruce.allison@ualberta.ca>

G. Benkart <benkart@math.wisc.edu>

Y. Gao <gao-yun@math.yale.edu>