Locally finite simple weight modules over twisted generalized Weyl algebras

• DOI: 10.1016/j.jalgebra.2006.05.036
• Publication Date: 2006-07-27T07:16:19Z
• Authors: Jonas T. Hartwig
• Keywords: Algebraically closed field; Verma module

We present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. When a certain commutative subalgebra is finitely generated over an algebraically closed field we obtain a classification of a class of locally finite simple weight modules as those induced from simple modules over a subalgebra isomorphic to a tensor product of noncommutative tori. As an application we describe simple weight modules over the quantized Weyl algebra.<br/>28 pages<br/>