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The multiplication theorem and bases in finite and affine quantum cluster algebras (1006.3928v4)
Published 20 Jun 2010 in math.RT, math.QA, and math.RA
Abstract: We prove a multiplication theorem for quantum cluster algebras of acyclic quivers. The theorem generalizes the multiplication formula for quantum cluster variables in \cite{fanqin}. We apply the formula to construct some $\mathbb{ZP}$-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 \cite{CK1} and \cite{DXX}).
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