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 Ãn. Furthermore, we provide a complete classification of cluster tilted algebras of type Ãn 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
Milestones
Received: 4 March 2010
Revised: 26 July 2010
Accepted: 31 August 2010
Published: 23 January 2012

Proposed: Andrei Zelevinsky
Seconded: Ravi Vakil, Bernd Sturmfels
Authors
Janine Bastian
Leibniz Universität Hannover
Institut für Algebra, Zahlentheorie und Diskrete Mathematik
Welfengarten 1
D-30167 Hannover
Germany