Operator algebras in rigid C*-tensor categories

Corey Jones (Australian National University)

Tuesday 17th January, 2017 16:00-17:00 Maths 204

Abstract

The ``trivial" tensor category of finite dimensional Hilbert spaces is the natural setting for finite dimensional multi-linear algebra.  A rigid C*-tensor category can be thought of as a generalization of this category, providing a model for finite dimensional multi-linear algebra with an underlying ``quantum symmetry".   In this talk, we will explain how to extend this analogy to the infinite dimensional world, providing notions of C* and W*- algebra objects internal to a tensor category C, which reduce to our familiar notions when C is trivial.  We will discuss how several objects and constructions from the theories of quantum groups and subfactors fit into this framework.  Based on joint work with Dave Penneys.

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