Locally Finite Simple Weight Modules over Twisted Generalized Weyl Algebras
نویسنده
چکیده
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.
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THESIS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Generalized Weyl algebras and elliptic quantum groups
This thesis consists of four papers. In the first paper we present methods and explicit formulas for describing simple weight modules over twisted generalized Weyl algebras. Under certain conditions we obtain a classification of a class of locally finite simple weight modules from simple modules over tensor products of noncommutative tori. As an application we describe simple weight modules ove...
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