Anomalous symmetries of classifiable C* algebras

Sergio Giron Pacheco (University of Oxford)

Thursday 25th March 16:00-17:00 Contact the Organizers for Zoom Coordinates

Abstract

Popa's classification of subfactors of the Hyperfinite II1 factor (R) with amenable standard invariant encompasses the classification of generalized symmetries of R, vastly generalizing the classification results of group actions on R by Connes, Jones and Ocneanu. Due to the recent classification of infinite dimensional, simple, seperable, unital C* algebras of finite nuclear dimension, satisfying the UCT, it is natural to consider to which extent the symmetries of R, both classical or quantum, carry over to the C*-setting. In this talk, I will discuss the existence question. It is known that any countable discrete group G acts faithfully on any classifiable C*-algebra. However, even for types of quantum symmetries closely related to group actions (anomalous symmetries) the existence question is subtle, and can have both positive and negative answers. I will discuss the algebraic K1 group of  a C*-algebra and how it acts as an obstruction to existence of anomalous symmetries. This is joint work with Sam Evington.

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