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Keywords:
quantum cluster algebra; $\mathbb {Z}[q^{\pm {1}/{2}}]$-basis; valued quiver
Summary:
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.
References:
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