论文标题
在无系数的量子簇代数的内泊托泊结构上
On inner Poisson structures of a quantum cluster algebra without coefficients
论文作者
论文摘要
本文的主要目的是表征没有系数的量子群集代数上的内泊松结构。主要是，我们证明没有系数的量子簇代数上的内泊托泊结构始终是标准的泊松结构。为了与兼容的泊松结构相关，我们在量子群集代数上介绍了所谓的局部泊松结构的概念，然后表明它等同于没有系数的情况下的局部标准泊松结构。根据\ cite {lp}的结果，在这种情况下，我们最终获得了局部内部泊松结构与兼容泊松结构之间的等效性。
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.
