On inner Poisson structures of a quantum cluster algebra without coefficients
Representation Theory
2020-08-13 v1 Rings and Algebras
Abstract
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. In order to relate with compatible 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 \cite{LP} we obtain finally the equivalence between locally inner Poisson structure and compatible Poisson structure in this case.
Cite
@article{arxiv.2008.05361,
title = {On inner Poisson structures of a quantum cluster algebra without coefficients},
author = {Fang Li and Jie Pan},
journal= {arXiv preprint arXiv:2008.05361},
year = {2020}
}
Comments
15 pages. arXiv admin note: substantial text overlap with arXiv:2003.12257