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An expansion formula for quantum cluster algebras from unpunctured triangulated surfaces

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Abstract

We generalize Musiker–Schiffler–Williams’ expansion formula to quantum cluster algebras from unpunctured surfaces. In particular, we give a combinatorial proof of the positivity for such class of quantum cluster algebras.

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Acknowledgements

The author is thankful to the anonymous reviewer for pointing out a gap in the original version. Thanks to S. Liu, I. Assem, T. Brüstle and D. Smith for financial support, thanks to Ilke Canakci for pointing their results on quantum Laurent expansion. Last, the author would take the opportunity to thanks his Ph.D. advisor Prof. Fang Li for continued encouragement these years. This project is partially supported by the National Natural Science Foundation of China (Nos. 12101617, 12071422, 11801043) and Guangdong Basic and Applied Basic Research Foundation 2021A1515012035 and the Fundamental Research Funds for the Central Universities, Sun Yat-sen University.

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  1. School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai, 519082, Guangdong, People’s Republic of China

    Min Huang

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Huang, M. An expansion formula for quantum cluster algebras from unpunctured triangulated surfaces. Sel. Math. New Ser. 28, 21 (2022). https://doi.org/10.1007/s00029-021-00750-2

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