A Z-basis for the cluster algebra associated to an affine quiver
Ding, Ming · Xiao, Jie · Xu, Fan
Original · EN
The canonical bases of cluster algebras of finite types and rank 2 are given explicitly in CK2005 and SZ respectively. In this paper, we will deduce Z-bases for cluster algebras for affine types Aₙ,ₙ,D and E. Moreover, we give an inductive formula for computing the multiplication between two generalized cluster variables associated to objects in a tube.
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