Marsh, RJ orcid.org/0000-0002-4268-8937 and Reiten, I (2016) Rigid and Schurian modules over cluster-tilted algebras of tame type. Mathematische Zeitschrift, 284 (3). pp. 643-682. ISSN 0025-5874
Abstract
We give an example of a cluster-tilted algebra Λ with quiver Q, such that the associated cluster algebra A(Q) has a denominator vector which is not the dimension vector of any indecomposable Λ-module. This answers a question posed by T. Nakanishi. The relevant example is a cluster-tilted algebra associated with a tame hereditary algebra. We show that for such a cluster-tilted algebra Λ, we can write any denominator vector as a sum of the dimension vectors of at most three indecomposable rigid Λ-modules. In order to do this it is necessary, and of independent interest, to first classify the indecomposable rigid Λ-modules in this case.
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Copyright, Publisher and Additional Information: | © Springer-Verlag Berlin Heidelberg 2016. This is an author produced version of a paper published in Mathematische Zeitschrift. The final publication is available at Springer via https://doi.org/10.1007/s00209-016-1668-z | ||||
Keywords: | Almost split sequences, cluster algebras, cluster categories, cluster-tilted algebras, c-vectors, d-vectors, Q-coloured quivers, tame hereditary algebras | ||||
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Institution: | The University of Leeds | ||||
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) | ||||
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Depositing User: | Symplectic Publications | ||||
Date Deposited: | 02 Feb 2016 12:54 | ||||
Last Modified: | 14 Apr 2017 03:14 | ||||
Published Version: | https://doi.org/10.1007/s00209-016-1668-z | ||||
Status: | Published | ||||
Publisher: | Springer Verlag | ||||
Identification Number: | https://doi.org/10.1007/s00209-016-1668-z |