In this paper we introduce a notion of quantum Hamiltonian (co)action of Hopf algebras endowed with Drinfel'd twist structure (resp., 2-cocycles). First, we define a classical Hamiltonian action in the setting of Poisson Lie groups compatible with the 2-cocycle stucture and we discuss a concrete example. This allows us to construct, out of the classical momentum map, a quantum momentum map in the setting of Hopf coactions and to quantize it by using Drinfel'd approach.

中文翻译：

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通过扭曲量化哈密顿量

在本文中，我们介绍了具有 Drinfel'd 扭曲结构（分别为 2-cocycle）的 Hopf 代数的量子哈密顿（共）作用的概念。首先，我们在与 2-cocycle 结构兼容的泊松李群的设置中定义了一个经典的哈密顿作用，并讨论了一个具体的例子。这允许我们从经典动量图构建一个在 Hopf 协同作用设置中的量子动量图，并使用 Drinfel'd 方法对其进行量化。