A $\mathbb{Z}$-basis for the cluster algebra associated to an affine quiver

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210473The canonical bases of cluster algebras of finite types and rank 2 are given explicitly in \cite{CK2005} and \cite{SZ} respectively. In this paper, we will deduce $\mathbb{Z}$-bases for cluster algebras for affine types $\widetilde{A}_{n,n},\widetilde{D}$ and $\widetilde{E}$. Moreover, we give an inductive formula for computing the multiplication between two generalized cluster variables associated to objects in a tube.21 pagesRepresentation TheoryRings and Algebras16G20, 16G99, 14M99, 13A99A $\mathbb{Z}$-basis for the cluster algebra associated to an affine quivertext