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On inner Poisson structures of a quantum cluster algebra without coefficients

  • Received: 01 July 2020 Revised: 01 January 2021 Published: 15 March 2021
  • 13F60, 46L65, 17B63

  • The main aim of this article is to characterize inner Poisson structure on a quantum cluster algebra without coefficients. Mainly, we prove that inner Poisson structure on a quantum cluster algebra without coefficients is always a standard Poisson structure. We introduce the concept of so-called locally inner Poisson structure on a quantum cluster algebra and then show it is equivalent to locally standard Poisson structure in the case without coefficients. Based on the result from [7] we obtain finally the equivalence between locally inner Poisson structure and compatible Poisson structure in this case.

    Citation: Fang Li, Jie Pan. On inner Poisson structures of a quantum cluster algebra without coefficients[J]. Electronic Research Archive, 2021, 29(5): 2959-2972. doi: 10.3934/era.2021021

    Related Papers:

  • The main aim of this article is to characterize inner Poisson structure on a quantum cluster algebra without coefficients. Mainly, we prove that inner Poisson structure on a quantum cluster algebra without coefficients is always a standard Poisson structure. We introduce the concept of so-called locally inner Poisson structure on a quantum cluster algebra and then show it is equivalent to locally standard Poisson structure in the case without coefficients. Based on the result from [7] we obtain finally the equivalence between locally inner Poisson structure and compatible Poisson structure in this case.



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  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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