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arXiv · 1412.6405

Rigid and Schurian modules over cluster-tilted algebras of tame type

Bethany Marsh·Idun Reiten
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Abstract

We give an example of a cluster-tilted algebra A with quiver Q, such that the associated cluster algebra has a denominator vector which is not the dimension vector of any indecomposable A-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 A, we can write any denominator vector as a sum of the dimension vectors of at most three indecomposable rigid A-modules. In order to do this it is necessary, and of independent interest, to first classify the indecomposable rigid A-modules in this case.

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Bethany Marsh, Idun Reiten. 2016-01-26. Rigid and Schurian modules over cluster-tilted algebras of tame type. https://arxiv.org/abs/1412.6405

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