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arXiv · 1608.05165

On Structure of cluster algebras of geometric type, II: Green's equivalences and paunched surfaces

Min Huang·Fang Li
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Abstract

Following our previous work [18], we introduce the notions of partial seed homomorphisms and partial ideal rooted cluster morphisms. Related to the theory of Green's equivalences, the isomorphism classes of sub-rooted cluster algebras of a rooted cluster algebra are corresponded one-by-one to the regular $\mathcal D$-classes of the semigroup consisting of partial seed endomorphisms of the initial seed. Moreover, for a rooted cluster algebra from a Riemannian surface, they are also corresponded to the isomorphism classes of the so-called paunched surfaces.

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Min Huang, Fang Li. 2016-08-18. On Structure of cluster algebras of geometric type, II: Green's equivalences and paunched surfaces. https://arxiv.org/abs/1608.05165

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