Noncommutative Geometry Seminar - Marcel Bischoff

October 21, 2016
Thursday, November 3, 2016 - 1:50pm to 2:50pm
Cockins Hall 240
math_sculpture

Title: Generalized orbifold construction for conformal nets

SpeakerMarcel Bischoff (Vanderbilt University)

Abstract: I will introduce the notion of a finite hypergroup and show that certain subfactors can naturally be seen as the fixed point algebra under an action of a hypergroup acting by unital completely positive maps. This has applications to local conformal nets of von Neumann algebras, which are an axiomatization of chiral conformal field theory. The well-known orbifold construction for conformal nets is the fixed points with respect to a proper action of a finite group of automorphisms. I will introduce a generalization of this construction to a finite hypergroup. It turns out that the fixed point net is a finite index subnet, and conversely, every finite index subnet is a generalized orbifold with respect to a unique hypergroup. In the case that the original net is assumed to be completely rational, we get several structural results. For example, if the net has trivial representation category, then the hypergroup comes from a fusion category F, and the representation category of the fixed point net is the Drinfeld center of F.

Based on arXiv:1506.02606

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