Counting cluster-tilted algebras of type $A_n$

Details Counting cluster-tilted algebras of type $A_n$ Counting cluster-tilted algebras of type $A_n$

2008-01-24

arxiv.org/abs/0801.3762v2

Mathematics

Representation Theory

9 pages, 4 figures, minor changes, grammatical corrections and layout

Scientific paper

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 $T=\tau^i T'$.

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