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Strongness of companion bases for cluster-tilted algebras of finite type


Authors: Karin Baur and Alireza Nasr-Isfahani
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
Published electronically: February 16, 2018
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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.


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Additional Information

Karin Baur
Affiliation: Institut für Mathematik und Wissenschaftliches Rechnen, Universität Graz, Heinrichstrasse 36, A-8010 Graz, Austria
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
Email: nasr_a@sci.ui.ac.ir, nasr@ipm.ir

DOI: https://doi.org/10.1090/proc/13977
Keywords: Cluster-tilted algebra, companion basis, indecomposable modules, dimension vector, relation-extension algebra, root system, Euler form
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
Article copyright: © Copyright 2018 American Mathematical Society

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