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

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

2010-06-20

arxiv.org/abs/1006.3928v4

Mathematics

Representation Theory

20 pages, the integral bases of cluster algebra of affine types are replaced

Scientific paper

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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