Czechoslovak Mathematical Journal, Vol. 61, No. 4, pp. 1077-1090, 2011

Bar-invariant bases of the quantum cluster
algebra of type $A^{(2)}_2$

Xueqing Chen, Ming Ding, Jie Sheng

X. Chen, Department of Mathematical and Computer Sciences, University of Wisconsin-Whitewater, 800 W. Main Street, Whitewater, WI 53190, U.S.A., e-mail: chenx@uww.edu; M. Ding, Center for Advanced Study, Tsinghua University, Beijing 10084, P. R. China, e-mail: m-ding04@mails.tsinghua.edu.cn; J. Sheng, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China, e-mail: shengjie@amss.ac.cn

Abstract: We construct bar-invariant $\mathbb{Z}[q^{\pm1/2}]$-bases of the quantum cluster algebra of the valued quiver $A^{(2)}_2$, one of which coincides with the quantum analogue of the basis of the corresponding cluster algebra discussed in P. Sherman, A. Zelevinsky: Positivity and canonical bases in rank 2 cluster algebras of finite and affine types, Moscow Math. J., 4, 2004, 947-974.

Keywords: quantum cluster algebra, $\mathbb{Z}[q^{\pm1/2}]$-basis, valued quiver

Classification (MSC 2010): 16G20, 20G42, 14M17


Full text available as PDF.

Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at myris@myris.cz.
Subscribers of Springer need to access the articles on their site, which is http://www.springeronline.com/10587.


[Previous Article] [Next Article] [Contents of This Number] [Contents of Czechoslovak Mathematical Journal]