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Bar-invariant bases of the quantum cluster algebra of type $A^{(2)}_2$
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 4, pp. 1077-1090
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We construct bar-invariant $\mathbb {Z}[q^{\pm {1}/{2}}]$-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.
We construct bar-invariant $\mathbb {Z}[q^{\pm {1}/{2}}]$-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.
DOI : 10.1007/s10587-011-0049-3
Classification : 13F60, 14M17, 16G10, 16G20, 16T20, 20G42
Keywords: quantum cluster algebra; $\mathbb {Z}[q^{\pm {1}/{2}}]$-basis; valued quiver 
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Chen, Xueqing; Ding, Ming; Sheng, Jie. Bar-invariant bases of the quantum cluster algebra of type $A^{(2)}_2$. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 4, pp. 1077-1090. doi: 10.1007/s10587-011-0049-3

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