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Maximal forward hom-orthogonal sequences for cluster-tilted algebras of finite type


Author: Alireza Nasr-Isfahani
Journal: Proc. Amer. Math. Soc. 147 (2019), 2775-2782
MSC (2010): Primary 16G20, 13F60; Secondary 05E10
DOI: https://doi.org/10.1090/proc/14523
Published electronically: April 9, 2019
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Abstract: Let $ \Lambda $ be a cluster-tilted algebra of finite type over an algebraically closed field and let $ B$ be one of the associated tilted algebras. We show that the $ B$-modules, ordered from right to left in the Auslander-Reiten quiver of $ \Lambda $ form a maximal forward hom-orthogonal sequence of $ \Lambda $-modules whose dimension vectors form the $ c$-vectors of a maximal green sequence for $ \Lambda $. Thus we give a proof of Igusa-Todorov's conjecture.


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Additional Information

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/14523
Keywords: Cluster-tilted algebras, forward hom-orthogonal sequences, maximal green sequences, Schurian modules, relation-extension algebras, cluster repetitive algebras
Received by editor(s): June 8, 2018
Received by editor(s) in revised form: September 16, 2018
Published electronically: April 9, 2019
Additional Notes: This research was supported in part by a grant from IPM (No. 96170417).
Communicated by: Jerzy Weyman
Article copyright: © Copyright 2019 American Mathematical Society