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arXiv · 1006.3928

The multiplication theorem and bases in finite and affine quantum cluster algebras

Ming Ding·Fan Xu
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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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Ming Ding, Fan Xu. 2010-06-20. The multiplication theorem and bases in finite and affine quantum cluster algebras. https://arxiv.org/abs/1006.3928

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