Linear Analysis Seminar

Date: February 9, 2018

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Mateusz Wasilewski, IMPAN

Title: Non-conjugacy of generator MASAs in q-Gaussian algebras

Abstract: In the study of group von Neumann algebras, sometimes maximal abelian subgroups give rise to maximal abelian subalgebras (MASAs); it happens so for free groups and abelian subgroups generated by a single free generator. These subalgebras are conjugate by an automorphism (coming from the automorphism of a free group), but not by an inner automorphism. Free group factors also admit a different representation, using Voiculescu's free Gaussian functor; in this setting one can generate a MASA using a vector from a real Hilbert space. Bożejko and Speicher introduced a deformation of free group factor, called the q-Gaussian algebras for which analogues of generator MASAs can be defined. I will show that these MASAs are never conjugate by an inner automorphism, using Popa's intertwining techniques (joint work with Martijn Caspers and Adam Skalski).