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Acyclic quantum cluster algebras via Hall algebras of morphisms

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Abstract

Let A be the path algebra of a finite acyclic quiver Q over a finite field. We realize the quantum cluster algebra with principal coefficients associated to Q as a sub-quotient of a certain Hall algebra involving the category of morphisms between projective A-modules.

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Notes

  1. The notations \(P_M\) and \(\Omega _M\) will be used throughout the paper.

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Acknowledgements

The authors are grateful to the anonymous referees for their valuable suggestions and comments, and supported partially by the National Natural Science Foundation of China (No.s 11771217, 11471177, 11801273), Natural Science Foundation of Jiangsu Province of China (No.BK20180722) and Natural Science Foundation of Jiangsu Higher Education Institutions of China (No.18KJB110017).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, People’s Republic of China

    Ming Ding

  2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People’s Republic of China

    Fan Xu

  3. Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, People’s Republic of China

    Haicheng Zhang

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  1. Ming Ding
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  2. Fan Xu
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  3. Haicheng Zhang
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Correspondence to Haicheng Zhang.

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Ding, M., Xu, F. & Zhang, H. Acyclic quantum cluster algebras via Hall algebras of morphisms. Math. Z. 296, 945–968 (2020). https://doi.org/10.1007/s00209-020-02465-0

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