Cluster characters for cyclic quivers

doi:10.1007/s11464-011-0146-5

Front Math Chin

2012, Vol. 7

Issue (4) : 679-693 https://doi.org/10.1007/s11464-011-0146-5

RESEARCH ARTICLE

Cluster characters for cyclic quivers

Ming DING¹, Fan XU²(

)

1. School of Mathematical Sciences, Nankai University, Tianjin 300071, China; 2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

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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.

Keywords Cyclic quiver cluster algebra ?-basis')" href="#">?-basis

Corresponding Author(s): XU Fan,Email:fanxu@mail.tsinghua.edu.cn

Issue Date: 01 August 2012

Cite this article:

Ming DING,Fan XU. Cluster characters for cyclic quivers[J]. Front Math Chin, 2012, 7(4): 679-693.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-011-0146-5
https://academic.hep.com.cn/fmc/EN/Y2012/V7/I4/679

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