The multiplication theorem and bases in finite and affine quantum cluster algebras
Abstract
We prove a multiplication theorem for quantum cluster algebras of acyclic quivers. The theorem generalizes the multiplication formula for quantum cluster variables in fanqin. We apply the formula to construct some ZP-bases in quantum cluster algebras of finite and affine types. Under the specialization q and coefficients to 1, these bases are the integral bases of cluster algebra of finite and affine types (see CK1 and DXX).
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