Counting cluster-tilted algebras of type $A_n$
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 $T=\tau^i T'$.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2008
- DOI:
- 10.48550/arXiv.0801.3762
- arXiv:
- arXiv:0801.3762
- Bibcode:
- 2008arXiv0801.3762A
- Keywords:
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- Mathematics - Representation Theory
- E-Print:
- 9 pages, 4 figures, minor changes, grammatical corrections and layout