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

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dc.creatorDing, Ming
dc.creatorXiao, Jie
dc.creatorXu, Fan
dc.date2008-11-22
dc.date2008-12-14
dc.date.accessioned2026-07-07T12:12:13Z
dc.date.available2026-07-07T12:12:13Z
dc.descriptionThe 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.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/0811.3676
dc.identifierhttp://arxiv.org/abs/0811.3676
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210473
dc.subjectRepresentation Theory
dc.subjectRings and Algebras
dc.subject16G20, 16G99, 14M99, 13A99
dc.titleA $\mathbb{Z}$-basis for the cluster algebra associated to an affine quiver
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