ENVELOPING-ALGEBRAS AND REPRESENTATIONS OF TOROIDAL LIE-ALGEBRAS

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 algebra as those whose universal enveloping algebras are non-Noetherian Ore domains.