The multiplication theorem and bases in finite and affine quantum cluster algebras
arXiv:1006.3928
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 -bases in quantum cluster algebras of finite and affine types. Under the specialization and coefficients to , these bases are the integral bases of cluster algebra of finite and affine types (see \cite{CK1} and \cite{DXX}).
20 pages, the integral bases of cluster algebra of affine types are replaced