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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Weight modules over infinite dimensional Weyl algebras


Authors: Vyacheslav Futorny, Dimitar Grantcharov and Volodymyr Mazorchuk
Journal: Proc. Amer. Math. Soc. 142 (2014), 3049-3057
MSC (2010): Primary 17B10, 17B65, 16D60
Published electronically: June 4, 2014
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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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Additional Information

Vyacheslav Futorny
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo SP, Brazil
Email: futorny@ime.usp.br

Dimitar Grantcharov
Affiliation: Department of Mathematics, University of Texas at Arlington, Arlington, Texas 76019
Email: grandim@uta.edu

Volodymyr Mazorchuk
Affiliation: Department of Mathematics, Uppsala University, Box 480, SE-751 06, Uppsala, Sweden
Email: mazor@math.uu.se

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-12071-5
PII: S 0002-9939(2014)12071-5
Received by editor(s): July 24, 2012
Received by editor(s) in revised form: October 8, 2012
Published electronically: June 4, 2014
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2014 American Mathematical Society