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Baur, K, Buan, AB and Marsh, RJ (2014) Torsion pairs and rigid objects in tubes. Algebras and Representation Theory, 17 (2). 565 - 591. ISSN 1386-923X
Abstract
We classify the torsion pairs in a tube category and show that they are in bijection with maximal rigid objects in the extension of the tube category containing the Prüfer and adic modules. We show that the annulus geometric model for the tube category can be extended to the larger category and interpret torsion pairs, maximal rigid objects and the bijection between them geometrically. We also give a similar geometric description in the case of the linear orientation of a Dynkin quiver of type A.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2013, Springer Verlag. This is an author produced version of a paper published in Algebras and Representation Theory. Uploaded in accordance with the publisher's self-archiving policy. The final publication is available at link.springer.com |
Keywords: | Tube category; torsion pair; torsion theory; pruefer module; adic module; annulus; maximal rigid object; arc model; direct limit; inverse limit |
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) |
Funding Information: | Funder Grant number EPSRC EP/G007497/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 27 Mar 2015 09:31 |
Last Modified: | 29 Mar 2018 04:47 |
Published Version: | http://dx.doi.org/10.1007/s10468-013-9410-6 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s10468-013-9410-6 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:83884 |
Available Versions of this Item
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Torsion Pairs and Rigid Objects in Tubes. (deposited 20 Nov 2013 12:47)
- Torsion pairs and rigid objects in tubes. (deposited 27 Mar 2015 09:31) [Currently Displayed]