Anomalous symmetries of classifiable C* algebras

Sergio Giron Pacheco (University of Oxford)

Thursday 25th March, 2021 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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