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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Classification of modules for infinite-dimensional string algebras
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by William Crawley-Boevey PDF
Trans. Amer. Math. Soc. 370 (2018), 3289-3313 Request permission

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.
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Additional Information
  • William Crawley-Boevey
  • Affiliation: Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
  • Address at time of publication: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
  • MR Author ID: 230720
  • Email: wcrawley@math.uni-bielefeld.de
  • Received by editor(s): March 7, 2016
  • Received by editor(s) in revised form: July 26, 2016
  • Published electronically: December 20, 2017
  • Additional Notes: This material is based upon work supported by the National Science Foundation under grant No. 0932078 000 while the author was in residence at the Mathematical Science Research Institute (MSRI) in Berkeley, California, during the spring semester 2013.
  • © Copyright 2017 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 3289-3313
  • MSC (2010): Primary 16D70; Secondary 13C05
  • DOI: https://doi.org/10.1090/tran/7032
  • MathSciNet review: 3766850