A study on quantum groups and von Neumann algebras concerning dual actions

我们利用冯·诺依曼代数的对偶作用研究了它们的作用。在这项研究中,我们证明了,任何相互作用的局部紧群K正确无限冯诺依曼代数和一个封闭的子群H (K,行动是闭上链共轭相互作用,来自一个强制H当且仅当的双重行动是由一个动作H .通过遍历测量等价子关系的可公度性的概念,我们还推广Hecke代数,冯·诺依曼代数的概念来自于测量等价关系。

We investigated actions on von Neumann algebra by their dual actions. In this study, we proved that, for any coaction of a locally compact group K on a properly infinite von Neumann algebra and a closed subgroup H of K, the action is cocycle conjugate to a coaction which comes from a coaction of H if and only if the dual action is induced by an action of H. By using the notion of commensurability of ergodic measured equivalence subrelations, we also generalized the notion of Hecke algebras to von Neumann algebras which come from measured equivalence relations.