The study of group actions on probability measure spaces occupies a central role in modern mathematics. If a group G acts on a probability measure space (X,µ), one can associate a von Neumann algebra, namely the crossed product von Neumann algebra. This von Neumann algebra naturally contains a copy of the group von Neumann algebra, denoted by L(G).

A far reaching conjecture of Neshveyev and Stormer predicts that the inclusion of the group von Neumann algebra L(G) inside the group measure space construction “remembers” the group and the action.

In my talk, I shall show that the conjecture is true for a large class of actions of i.c.c. groups. This talk is based on a joint work with Prof. Ionut Chifan.

Sayan Das，华东师范大学数学学院青年研究员，国家级青年人才。2017年博士毕业于美国Vanderbilt大学，导师Jesse Peterson & Vaughan Jones。研究方向为算子代数，论文发表在Amer. J. Math, Math. Ann., Compos. Math., Trans. Amer. Math. Soc., Anal. PDE, J. Funct. Anal.等数学期刊。