Mutation classes of Ãn-quivers and derived equivalence classification of cluster tilted algebras of type Ãn

Bastian, Janine

doi:10.2140/ant.2011.5.567

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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

DOI: 10.2140/ant.2011.5.567

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

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

Vol. 5, No. 5, 2011