RESEARCH ARTICLE

Cluster characters for cyclic quivers

  • Ming DING 1 ,
  • Fan XU , 2
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  • 1. School of Mathematical Sciences, Nankai University, Tianjin 300071, China
  • 2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received date: 10 May 2010

Accepted date: 29 May 2011

Published date: 01 Aug 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

We define an analogue of the Caldero-Chapoton map for the cluster category of finite-dimensional nilpotent representations over a cyclic quiver. We prove that it is a cluster character and satisfies some inductive formulas for the multiplication between the generalized cluster variables (the images of objects of the cluster category under this map). Moreover, we construct a -basis for the algebra generated by all generalized cluster variables.

Cite this article

Ming DING , Fan XU . Cluster characters for cyclic quivers[J]. Frontiers of Mathematics in China, 2012 , 7(4) : 679 -693 . DOI: 10.1007/s11464-011-0146-5

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