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arXiv · 0801.3762

Counting cluster-tilted algebras of type $A_n$

Hermund André Torkildsen
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Abstract

The purpose of this paper is to give an explicit formula for the number of non-isomorphic cluster-tilted algebras of type $A_n$, by counting the mutation class of any quiver with underlying graph $A_n$. It will also follow that if $T$ and $T'$ are cluster-tilting objects in a cluster category $\mathcal{C}$, then $\End_{\mathcal{C}}(T)$ is isomorphic to $\End_{\mathcal{C}}(T')$ if and only if $T=τ^i T'$.

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BibTeXRIS

Hermund André Torkildsen. 2008-04-16. Counting cluster-tilted algebras of type $A_n$. https://arxiv.org/abs/0801.3762

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