A ℤ-basis for the cluster algebra associated to an affine quiver

2008/11/22 by Ding, Ming, Xiao, Jie, Xu, Fan
#13A99 #14M99 #16G20 #16G99 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0811.3676

Abstract

The canonical bases of cluster algebras of finite types and rank 2 are given explicitly in \citeCK2005 and \citeSZ respectively. In this paper, we will deduce ℤ-bases for cluster algebras for affine types \widetildeA_n,n,\widetildeD and \widetildeE. 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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