Operator algebras in rigid C*-tensor categories
Corey Jones (Australian National University)
Tuesday 17th January, 2017 16:00-17:00 Maths 204
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.