Decomposition of persistence modules
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- by Magnus Bakke Botnan and William Crawley-Boevey
- Proc. Amer. Math. Soc. 148 (2020), 4581-4596
- DOI: https://doi.org/10.1090/proc/14790
- Published electronically: August 14, 2020
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Abstract:
We show that a pointwise finite-dimensional persistence module indexed over a small category decomposes into a direct sum of indecomposables with local endomorphism rings. As an application of this result we give new, short proofs of fundamental structure theorems for persistence modules.References
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Bibliographic Information
- Magnus Bakke Botnan
- Affiliation: Department of Mathematics, VU University Amsterdam, The Netherlands
- MR Author ID: 1002262
- Email: m.b.botnan@vu.nl
- William Crawley-Boevey
- Affiliation: Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
- MR Author ID: 230720
- Email: wcrawley@math.uni-bielefeld.de
- Received by editor(s): November 21, 2018
- Received by editor(s) in revised form: January 16, 2019, and June 24, 2019
- Published electronically: August 14, 2020
- Additional Notes: The first author was supported by the DFG Collaborative Research Center SFB/TR 109 “Discretization in Geometry and Dynamics”.
The second author was supported by the Alexander von Humboldt Foundation in the framework of an Alexander von Humboldt Professorship endowed by the German Federal Ministry of Education and Research. - Communicated by: Jerzy Weyman
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 4581-4596
- MSC (2020): Primary 16G20; Secondary 55N31
- DOI: https://doi.org/10.1090/proc/14790
- MathSciNet review: 4143378