- Aldo Garcia Guinto, MSU
- Free Stein dimension of crossed products by finite groups
- 02/06/2023
- 4:00 PM - 5:30 PM
- C517 Wells Hall
- Brent Nelson (banelson@msu.edu)
In this talk, we will discuss a free probabilistic quantity called free Stein dimension and compute it for a crossed product by a finite group. The free Stein dimension is the Murray-von Neumann dimension of a particular subspace of derivations. Charlesworth and Nelson defined this quantity in the hope of finding a von Neumann algebra invariant. While it is still not known to be a von Neumann algebra invariant, it is an invariant for finitely generated unital tracial *-algebras and algebraic methods have been more successful than analytic ones in studying it. Our result continues this trend, and reveals a formula for the free Stein dimension of a crossed product by a finite group that is reminiscint of the Schreier formula for a finite index subgroups of free groups.
