Title: Discrete inclusions of simple C*-algebras
Speaker: Roberto Hernandez Palomares (Waterloo)
Abstract: A subfactor is a unital inclusion of simple von Neumann algebras, and their 'size' is measured by the Jones index. Vaughan Jones proved the striking Index Rigidity Theorem establishing the set of values the index takes is exactly $\{4\cos^2(\pi/n)\}_{n\geq 3}\cup [4, \infty]$. This discovery started the modern theory of subfactors and their classification program.
Discrete subfactors conform an ample and well-behaved class resembling the properties of discrete groups. These subfactors are studied through the Standard Invariant --which we view as an action of a unitary tensor category together with a chosen generator-- and can be reconstructed from it. In this talk, I will define discreteness for inclusions of simple C*-algebras and establish a theorem stating that --similarly to their von Neumann counterparts,-- these can be reconstructed from a Standard Invariant. This is work in progress, joint with Brent Nelson and Matthew Lorentz.
