Weight modules over infinite dimensional Weyl algebras

2012/07/24 by Vyacheslav Futorny, Futorny, Vyacheslav, Dimitar Grantcharov +3 · 1 citation
Mathematics · #16D60 #17B10 #17B65 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:16D60 #msc:17B10 #msc:17B65

paper · pdf · doi:10.48550/arxiv.1207.5780

10 pages

openalex publication_date 2012/07/24 · arxiv created 2012/10/19 · arxiv updated 2012/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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