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On structure of cluster algebras of geometric type I: In view of sub-seeds and seed homomorphisms

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Abstract

Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for (rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also, we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11671350 and 11571173). The authors thank the referees for many helpful comments and suggestions in improving the quality and readability of this paper.

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Author notes

  1. Min Huang

    Present address: Current address: Département de Mathématiques, Université de Sherbrooke, Sherbrooke, J1K 2R1, Canada

  2. Yichao Yang

    Present address: Current address: School of Mathematics and Statistics, Changshu Institute of Technology, Suzhou, 215500, China

Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Min Huang & Fang Li

  2. Département de Mathématiques, Université de Sherbrooke, Sherbrooke, J1K 2R1, Canada

    Yichao Yang

Authors
  1. Min Huang
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  2. Fang Li
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  3. Yichao Yang
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Correspondence to Fang Li.

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Huang, M., Li, F. & Yang, Y. On structure of cluster algebras of geometric type I: In view of sub-seeds and seed homomorphisms. Sci. China Math. 61, 831–854 (2018). https://doi.org/10.1007/s11425-016-9100-8

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  • DOI: https://doi.org/10.1007/s11425-016-9100-8

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