Vol. 5, No. 5, 2011

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Mutation classes of $\tilde{A}_n$-quivers and derived equivalence classification of cluster tilted algebras of type $\tilde{A}_n$

Janine Bastian

Vol. 5 (2011), No. 5, 567–594
Abstract

We give an explicit description of the mutation classes of quivers of type ${Ã}_{n}$. Furthermore, we provide a complete classification of cluster tilted algebras of type ${Ã}_{n}$ up to derived equivalence. We show that the bounded derived category of such an algebra depends on four combinatorial parameters of the corresponding quiver.

Keywords
cluster tilted algebra, quiver mutation, derived equivalence
Mathematical Subject Classification 2000
Primary: 16G20
Secondary: 18E35, 18E30