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Mathematische Zeitschrift

, Volume 265, Issue 4, pp 951–970 | Cite as

Cluster structures from 2-Calabi–Yau categories with loops

  • Aslak Bakke Buan
  • Robert J. Marsh
  • Dagfinn F. VatneEmail author
Article

Abstract

We generalise the notion of cluster structures from the work of Buan–Iyama–Reiten–Scott to include situations where the endomorphism rings of the clusters may have loops. We show that in a Hom-finite 2-Calabi–Yau category, the set of maximal rigid objects satisfies these axioms whenever there are no 2-cycles in the quivers of their endomorphism rings. We apply this result to the cluster category of a tube, and show that this category forms a good model for the combinatorics of a type B cluster algebra.

Keywords

Direct Summand Cluster Structure Endomorphism Ring Cluster Algebra Rigid Object 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Aslak Bakke Buan
    • 1
  • Robert J. Marsh
    • 2
  • Dagfinn F. Vatne
    • 1
    Email author
  1. 1.Institutt for Matematiske FagNorges Teknisk-Naturvitenskapelige UniversitetTrondheimNorway
  2. 2.Department of Pure MathematicsUniversity of LeedsLeedsUK

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