Twisted Weyl algebras, crossed products, and representations

Details Twisted Weyl algebras, crossed products, and representations Twisted Weyl algebras, crossed products, and representations

2010-05-03

arxiv.org/abs/1005.0341v2

Mathematics

Rings and Algebras

The paper has been withdrawn. It will be substituted by two modified papers by the same authors

Scientific paper

We prove that any twisted generalized Weyl algebra satisfying certain consistency conditions can be embedded into a crossed product. We also introduce a new family of twisted generalized Weyl algebras, called multiparameter twisted Weyl algebras, for which we parametrize all simple quotients of a certain kind. Both Jordan's simple localization of the multiparameter quantized Weyl algebra and Hayashi's $q$-analog of the Weyl algebra are special cases of this construction. We classify all simple weight modules over any multiparameter twisted Weyl algebra. Extending results by Benkart and Ondrus, we also describe all Whittaker pairs up to isomorphism over a class of twisted generalized Weyl algebras which includes the multiparameter twisted Weyl algebras.

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