Bavula, V.V., Bekkert, V. and Futorny, V. (Submitted: 2019) Explicit description of generalized weight modules of the algebra of polynomial integro-differential operators In. arXiv. (Submitted)
Abstract
For the algebra In of polynomial integro-differential operators over a field K of characteristic zero, a classification of simple weight and generalized weight (left and right) In-modules is given. It is proven that the category of weight In-modules is semisimple. An explicit description of generalized weight In-modules is given and using it a criterion is obtained for the problem of classification of indecomposable generalized weight In-modules to be of finite representation type, tame or wild. In the tame case, a classification of indecomposable generalized weight In-modules is given. In the wild case `natural` tame subcategories are considered with explicit description of indecomposable modules. It is proven that every generalized weight In-module is a unique sum of absolutely prime modules. For an arbitrary ring R, we introduce the concept of {\em absolutely prime} R-module (a nonzero R-module M is absolutely prime if all nonzero subfactors of M have the same annihilator). It is shown that every indecomposable generalized weight In-module is equidimensional. A criterion is given for a generalized weight In-module to be finitely generated.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019 The Author(s). For reuse permissions, please contact the Author(s). |
Keywords: | The algebra of polynomial integro-differential operators; weight and generalized weight modules; indecomposable module; simple module; finite representation type; tame and wild |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 12 Jun 2019 13:52 |
Last Modified: | 12 Jun 2019 13:52 |
Published Version: | https://arxiv.org/abs/1906.00385 |
Status: | Submitted |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:147254 |