Swiss Knots 2011

Knot Theory and Algebra

Lake Thun, May 23-27

Associators and the Quantization of Lie Bialgebras

Prof. Dr. David A. Kazhdan's talk
Date: 24.05.11   Time: 15.00 - 15.50   Room: Gwatt Zentrum

Coauthor: Etingof

Abstract: The strongest algebraic input to quantum topology comes from the theory of quantum groups, and much of the theory of quantum groups comes from the fact that Lie bialgebras can always be quantized. Yet topologists have no "internal" understanding of quantum groups and of the quantization of Lie bialgebras; they take these as packaged boxes coming from the outside. In my talk I will sketch the initial parts of the Etingof-Kazhdan (EK) theory of quantization of Lie bialgebras. I hope to review the relevant definitions and to explain how a Drinfel'd associator (itself a knot theoretic object) can be used to quantize the double of a Lie bialgebra L in a "universal" manner, and possibly to sketch how L itself can be quantized using "acyclic" formulas. In his lecture, Bar-Natan will describe his plans/failures/dreams of interpreting the EK theory within the theory of virtual knots.