The wondrous world of hyperfinite subfactors


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March 30, 2021 10:00 am - 11:00 am
via Zoom Video Conferencing

Dietmar Bisch - Vanderbilt University

The hyperfinite II1 factor contains a wealth of subfactors, many of which give rise to new and fascinating mathematical structures. For instance, the standard representation of a subfactor generates a certain unitary tensor category that Jones described as (what he called) a "planar algebra." It is a complete invariant for amenable, hyperfinite subfactors due to a deep result of Popa. However, generic subfactors are not amenable, and one typically does not know how to distinguish them. I will discuss a notion of "noncommutativity'' for a subfactor that provides an invariant that is complementary to the planar algebra. Bare hand constructions of hyperfinite subfactors generally lead to "commutative'' examples, and I will explain a theorem that allows us to produce "very noncommutative'' ones as well. It involves actions of suitable groups on the hyperfinite II1 factor.