标题： 紧量子群的作用 显示英文标题

标题： Actions of compact quantum groups

摘要： 这些讲义是为2015年贝德拉沃“拓扑量子群”暑期学校准备的，涉及紧致量子群作用于C*-代数（“局部紧致量子空间”）理论的各个方面。 在回顾了典型分量和约化与普遍完成的基本概念之后，我们研究了交叉积和 smash 积 C*-代数，直至提出 Takesaki-Takai-Baaj-Skandalis 对偶性（在代数框架下）。 然后我们研究了两种特殊类型的量子群作用，即齐次作用和自由作用。 我们探讨了结合这两种类型的量子扭子，并证明更一般地，任何齐次作用都可以扩展为具有离散经典“量子轨道集”的自由作用。最后，我们用组合方法描述了自由正交量子群的齐次作用。 显示英文摘要

摘要： These lecture notes, prepared for the summer school "Topological quantum groups", Bedlewo 2015, deal with aspects of the theory of actions of compact quantum groups on C*-algebras ('locally compact quantum spaces'). After going over the basic notions of isotypical components and reduced and universal completions, we look at crossed and smash product C*-algebras, up to the statement of the Takesaki-Takai-Baaj-Skandalis duality (in the algebraic setting). We then look at two special types of actions, namely homogeneous actions and free actions. We study the actions which combine both types, the quantum torsors, and show that more generally any homogeneous action can be completed to a free action with a discrete, classical set of `quantum orbits'. We end with a combinatorial description of the homogeneous actions for the free orthogonal quantum groups.