Abstract
We construct bar-invariant ℤ[q ±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.
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