Crawley-Boevey, W (2018) Classification of modules for infinite-dimensional string algebras. Transactions of the American Mathematical Society, 370 (5). pp. 3289-3313. ISSN 0002-9947
Abstract
We relax the definition of a string algebra to also include infinite-dimensional algebras such as k[x,y]/(xy). Using the functorial filtration method, which goes back to Gelfand and Ponomarev, we show that finitely generated modules and artinian modules (and more generally finitely controlled and pointwise artinian modules) are classified in terms of string and band modules. This subsumes the known classifications of finite-dimensional modules for string algebras and of finitely generated modules for k[x,y]/(xy). Unlike in the finite-dimensional case, the words parameterizing string modules may be infinite.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 American Mathematical Society. First published in Transactions of the American Mathematical Society, Volume 370/5, May 2018, published by the American Mathematical Society. |
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: | 28 Jul 2016 14:05 |
Last Modified: | 20 Apr 2018 07:52 |
Status: | Published |
Publisher: | American Mathematical Society |
Identification Number: | 10.1090/tran/7032 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:103043 |