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

通过对偶作用研究了von Neumann代数上的作用。在这项研究中，我们证明了对于局部紧群K在真无限von Neumann代数和K的闭子群H上的任何余作用，该作用是由H的余作用产生的余作用的余圈共轭当且仅当对偶作用是由H的作用诱导的。利用遍历度量等价关系的公度概念，我们还将Hecke代数的概念推广到来自度量等价关系的von Neumann代数。

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.