Baur, K orcid.org/0000-0002-7665-476X and Torkildsen, HA (2020) A Geometric Interpretation of Categories of Type à and of Morphisms in the Infinite Radical. Algebras and Representation Theory, 23. pp. 657-692. ISSN 1386-923X
Abstract
We give a geometric realization of the module category of a hereditary algebra of type A~A~. We work with oriented arcs to define a translation quiver isomorphic to the Auslander-Reiten quiver of the module category of type A~A~. To get a description of the module category, we introduce long moves between arcs. These allow us to include the infinite radical in the geometric description. Finally, our results can also be used to describe the corresponding cluster categories by taking unoriented arcs instead.
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Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
Keywords: | Tame module category; Cluster category; Infinite radical; AR quiver |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 04 May 2022 14:52 |
Last Modified: | 04 May 2022 14:52 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s10468-019-09863-x |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:186469 |
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