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
MathSciNet review:
3778144
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Abstract | References | Similar Articles | Additional Information
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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-vectors of cluster algebras of finite type, Electron. J. Combin. 21 (2014), no. 1, Paper 1.3, 107. Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 16G10, 16G20, 13F60, 16S70, 05E10
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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
