Strongness of companion bases for cluster-tilted algebras of finite type
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- by Karin Baur and Alireza Nasr-Isfahani PDF
- Proc. Amer. Math. Soc. 146 (2018), 2409-2416 Request permission
Abstract:
For every cluster-tilted algebra of simply-laced Dynkin type we provide a companion basis which is strong, i.e., gives the set of dimension vectors of the finitely generated indecomposable modules for the cluster-tilted algebra. This shows in particular that every companion basis of a cluster-tilted algebra of simply-laced Dynkin type is strong. Thus we give a proof of Parsons’s conjecture.References
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Additional Information
- Karin Baur
- Affiliation: Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Heinrichstrasse 36, A-8010 Graz, Austria
- MR Author ID: 724373
- ORCID: 0000-0002-7665-476X
- Email: baurk@uni-graz.at
- Alireza Nasr-Isfahani
- Affiliation: Department of Mathematics, University of Isfahan, P.O. Box 81746-73441, Isfahan, Iran—and—School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
- MR Author ID: 634713
- Email: nasr_a@sci.ui.ac.ir, nasr@ipm.ir
- Received by editor(s): March 15, 2017
- Received by editor(s) in revised form: July 31, 2017, and September 10, 2017
- Published electronically: February 16, 2018
- Communicated by: Jerzy Weyman
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2409-2416
- MSC (2010): Primary {16G10}, {16G20}, {13F60}, {16S70}; Secondary {05E10}
- DOI: https://doi.org/10.1090/proc/13977
- MathSciNet review: 3778144