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September 2, 2022

Subfactor Seminar-On the invariant subalgebra rigidity (ISR) property

A group factor L(G) is said to have the ISR property, if every G invariant von Neumann subalgebra of L(G) arises from a normal subgroup of G.

In this talk I will show that every G-invariant subfactor arises from a normal subgroup. I will also provide examples of a large class of icc groups, including hyperbolic groups, and nonamenable groups with positive first L^2-Betti number (containing an infinite amenable subgroup) whose corresponding group factors satisfy the ISR property.  I will also mention some applications towards the study of invariant subalgebras of group C*-algebras, and discuss a few open problems.

This talk is based on a recent joint work with Prof. Ionut Chifan and Bin Sun.