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Indecomposable generalized weight modules over the algebra of polynomial integro-differential operators


Authors: V. Bavula, V. Bekkert and V. Futorny
Journal: Proc. Amer. Math. Soc. 146 (2018), 2373-2380
MSC (2010): Primary 16D60, 16D70, 16P50, 16U20
DOI: https://doi.org/10.1090/proc/13985
Published electronically: January 29, 2018
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Abstract: For the algebra $ \mathbb{I}_1= K\langle x, \frac {d}{dx}, \int \rangle $ of polynomial integro-differential operators over a field $ K$ of characteristic zero, a classification of indecomposable, generalized weight $ \mathbb{I}_1$-modules of finite length is given. Each such module is an infinite dimensional uniserial module. Ext-groups are found between indecomposable generalized weight modules; it is proven that they are finite dimensional vector spaces.


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Additional Information

V. Bavula
Affiliation: Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom
Email: v.bavula@sheffield.ac.uk

V. Bekkert
Affiliation: Departamento de Matemática, ICEx, Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627, CP 702, CEP 30123-970, Belo Horizonte-MG, Brasil
Email: bekkert@mat.ufmg.br

V. Futorny
Affiliation: Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, São Paulo, CEP 05315-970, Brasil
Email: futorny@ime.usp.br

DOI: https://doi.org/10.1090/proc/13985
Keywords: The algebra of polynomial integro-differential operators, generalized weight module, indecomposable module, simple module.
Received by editor(s): January 28, 2017
Received by editor(s) in revised form: August 27, 2017
Published electronically: January 29, 2018
Communicated by: Kailash Misra
Article copyright: © Copyright 2018 American Mathematical Society

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