Planar algebras associated to cocommuting squares
Organizers
Speaker
Junhwi Lim
Time
Wednesday, November 19, 2025 10:30 AM - 12:00 PM
Venue
A3-3-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
The ‘generalized symmetries’ of subfactors are encoded by their planar algebras. A natural foundational question is “What minimal structure can be universally expected from these symmetries?” For arbitrary subfactors, Jones showed that the associated planar algebra contains the Temperley-Lieb-Jones algebra. When an intermediate subfactor is present, the planar algebra contains the Fuss-Catalan-Bisch-Jones algebra, introduced by Bisch and Jones. However, the situation with two intermediate subfactors remains an open problem. As a natural special case, we study cocommuting squares of factors with ‘group-like’ properties. We exhibit the skein relations of their associated planar algebras and show that these algebras extend the partition algebras. This is based on a joint work with Dietmar Bisch.