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On Structure of Cluster Algebras of Geometric Type, II: Green's Equivalences and Paunched Surfaces

Min Huang Zhejiang University Fang Li Zhejiang University

Representation Theory mathscidoc:1702.30001

Pure and Applied Mathematics Quarterly, 11, (3), 40, 2015
Following our previous work \cite{HLY}, 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.
seed homomorphism, rooted cluster morphism, sub-rooted cluster algebra, Green's equivalence, paunched surface
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@inproceedings{min2015on,
  title={On Structure of Cluster Algebras of Geometric Type, II: Green's Equivalences and Paunched Surfaces},
  author={Min Huang, and Fang Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170210003818952782416},
  booktitle={Pure and Applied Mathematics Quarterly},
  volume={11},
  number={3},
  pages={40},
  year={2015},
}
Min Huang, and Fang Li. On Structure of Cluster Algebras of Geometric Type, II: Green's Equivalences and Paunched Surfaces. 2015. Vol. 11. In Pure and Applied Mathematics Quarterly. pp.40. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170210003818952782416.
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