Weight Modules over Exp-polynomial Lie Algebras

In this paper, we generalize a result by Berman and Billig on weight modules over Lie algebras with polynomial multiplication. More precisely, we show that a highest weight module with an exp-polynomial “highest weight” has finite dimensional weight spaces. We also get a class of irreducible weight modules with finite dimensional weight spaces over generalized Virasoro algebras which do not occur over the classical Virasoro algebra. 0. Introduction. Representations of affine Lie algebras and the Virasoro algebra have many important applications in mathematics and physics. One of the main ingredients of these theories is the construction of the highest weight modules. Recently there has been substantial activity in developing representation theories for higher rank 2000 Mathematics Subject Classification. 17B10, 17B65, 17B70.