Weight modules over infinite dimensional Weyl algebras

Futorny, Vyacheslav; Grantcharov, Dimitar; Mazorchuk, Volodymyr

doi:10.1090/S0002-9939-2014-12071-5

Weight modules over infinite dimensional Weyl algebras
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by Vyacheslav Futorny, Dimitar Grantcharov and Volodymyr Mazorchuk PDF

Proc. Amer. Math. Soc. 142 (2014), 3049-3057 Request permission

Abstract:

We classify simple weight modules over infinite dimensional Weyl algebras and realize them using the action on certain localizations of the polynomial ring. We describe indecomposable projective and injective weight modules and deduce from this a description of blocks of the category of weight modules by quivers and relations. As a corollary we establish Koszulity for all blocks.

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