Probabilistic Operator Algebra Seminar: Standard invariants for discrete subfactors

Seminar | March 12 | 2-3:50 p.m. | 736 Evans Hall

 Dave Penneys, Ohio State University

 Department of Mathematics

The standard invariant of a finite index $II_1$ subfactor is a λ-lattice and forms a planar algebra. In turn, the planar algebra formalism has been helpful in constructing and classifying subfactors, as well as studying analytic properties. In joint work with Corey Jones, we give a well-behaved notion of the standard invariant of an extremal irreducible discrete subfactor $N\subset M$, where $N$ is type $II_1$ and $M$ is an arbitrary factor. We also get a subfactor reconstruction theorem. This generalizes the standard invariant for finite index subfactors to a natural class of infinite index subfactors. Particular examples include the symmetric enveloping inclusion and examples coming from discrete quantum groups.