## Mathematical Physics and Operator Algebras

•  Rolando de Santiago, Purdue University
•  Groups, Group Actions, and von Neumann Algebras
•  04/15/2021
•  5:00 PM - 5:50 PM
•  Online (virtual meeting) (Virtual Meeting Link)
•  Brent Nelson (banelson@msu.edu)

Given a group $G$ acting on measure space $(X,\mu)$ Murray and von Neumann’s group-measure space construction describes a von Neumann algebra $L^\infty(X,\mu)\rtimes G$ which encodes both the group, the space and the action. The special case where the space is a singleton and the action is trivial produces the group von Neumann algebra $L(G)$. In this talk, we will aim to describe properties of $L^\infty(X,\mu)\rtimes G$ in terms of the group, the space and the action; compute $L^\infty(X,\mu)\rtimes G$ in special cases; and describe how the group-measure space varies or the group von Neumann algebra varies with $G$. All this serves to illustrate the fundamental problem in this area: von Neumann algebras tend to have poor memory of their generating data. This talk assumes a working knowledge of group theory and linear algebra, and while knowledge of measure theory may be helpful, it is not required.

## Contact

Department of Mathematics
Michigan State University