Frontiers of Mathematics in China >

2011 , Vol. 6 >Issue 2: 231 - 240

DOI: https://doi.org/10.1007/s11464-011-0104-2

RESEARCH ARTICLE

On quantum cluster algebras of finite type

  • Ming DING
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  • Institute for Advanced Study, Tsinghua University, Beijing 100084, China

Received date: 24 Oct 2010

Accepted date: 08 Jan 2011

Published date: 01 Apr 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We extend the definition of a quantum analogue of the Caldero-Chapoton map defined by D. Rupel. When Q is a quiver of finite type, we prove that the algebra ℋ|k|(Q) generated by all cluster characters is exactly the quantum cluster algebra ℰℋ|k|(Q).

Key words： Cluster variable; quantum cluster algebra

Cite this article

Ming DING . On quantum cluster algebras of finite type[J]. Frontiers of Mathematics in China, 2011 , 6(2) : 231 -240 . DOI: 10.1007/s11464-011-0104-2

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