Swiss Knots 2011

Knot Theory and Algebra

Lake Thun, May 23-27

An intriguing duality in planar algebra algebra

Prof. Dr. Vaughan F.R. Jones's talk
Date: 23.05.11   Time: 09.00 - 09.50   Room: Gwatt Zentrum

Abstract: A planar algebra structure defines many different algebra structures, the one most studied being the inductive limit where the algebras are included in the same way the braid groups (or more generally tangle algebras) are. But one may also form a graded algebra with multiplication being just "concatenation". In both cases a pictorially defined subalgebra allows one to recover the entire planar algebra structure, but the algebras themselves are radically different-one is locally finite dimensional and the other contains no finite dimensional subalgebras. One is related to braids and the other to random matrices. Both admit natural related structures that give a braided "quantum double". I will present both constructions and the pi/2 rotation that seems to connect them.