Classical limits of quantum groups give rise to multiplicative Poisson structures such as Poisson-Lie and quasi-Poisson structures. We relate them to the notion of a shifted Poisson structure which gives a conceptual framework for understanding classical (dynamical) r-matrices, quasi-Poisson groupoids and so on. We also propose a notion of a symplectic realization of shifted Poisson structures and show that Manin pairs and Manin triples give examples of such.

中文翻译：

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泊松-李结构转变为泊松结构

量子群的经典极限产生了可乘泊松结构，例如泊松-李和准泊松结构。我们将它们与位移泊松结构的概念相关联，该泊松结构为理解经典（动态）r矩阵，拟泊松群群等提供了概念框架。我们还提出了变位Poisson结构的辛实现的概念，并表明Manin对和Manin三元组给出了这种例子。