COUNTING CLUSTER-TILTED ALGEBRAS OF TYPE An

Year 2008, Volume: 4 Issue: 4, 149 - 158, 01.12.2008

Hermund André Torkildsen

Abstract

The purpose of this paper is to give an explicit formula for the number of non-isomorphic cluster-tilted algebras of type An, by counting the mutation class of any quiver with underlying graph An. It will also follow that if T and T0 are cluster-tilting objects in a cluster category C, then EndC(T) is isomorphic to EndC(T0) if and only if T = τiT0.

Keywords

Cluster category, cluster-tilted algebra, quiver, mutation, mutation class, triangulation of polygons, Catalan number