Enveloping algebras and representations of toroidal Lie algebras

Stephen Berman and Ben Cox

Vol. 165 (1994), No. 2, 239–267

DOI: 10.2140/pjm.1994.165.239

Abstract

This paper is about Toroidal Lie algebras which generalize the notion of an Affine Lie algebra. We study Verma type modules for these Toroidal algebras and prove an irreducibility criterion when the number of variables is two. We use the fact that the universal enveloping algebra is an Ore domain to obtain facts about the Verma type modules. Moreover, we are able to characterize the Affine Kac-Moody Lie algebras as those whose universal enveloping algebras are non-Noetherian Ore domains.

Mathematical Subject Classification 2000

Primary: 17B35

Secondary: 17B10

Milestones

Received: 3 June 1992

Accepted: 21 December 1992

Published: 1 October 1994