The Peterson-Thom conjecture states that given an amenable subgalebra of a free group factor, there is a unique maximal amenable subalgebra containing it (unique is the hard part). Equivalently, given two diffuse, amenable subalgebras with diffuse intersection, the algebra they generate is amenable. I will discuss some random matrix problems related to the Haagerup-Thorbjornsen theorem that would solve the problem affirmatively, if true.
Copyright. All Rights Reserved.