The
Centre for Mathematical
Physics
SEMINAR
Speaker: Liam Wagner, CMP, UQ
Title: Representations of finite groups and pre-monoidal categories
10am,
Wednesday 26 October, 2005
blding 67, room 641
Abstract:
An algebraic formulation was found which showed that it is possible to
define a symmetric, pre-monoidal structure (where associativity and monoidality are
explicitly broken) for the category of representations of an arbitrary Lie
algebra, where the statistics are prescribed by a Casimir
invariant K. The procedure, known as twining, was specifically introduced to
break the quasi-bialgebra structure of the universal
enveloping algebras of semi-simple Lie algebras in such a way that the category
of finite-dimensional representations is pre-monoidal.
We have subsequently found that similar procedures can be used for
categories of representations of finite groups.
A key difference between the finite group and Lie algebra cases is that
for finite groups there is a well developed theory of characters which makes it
possible to completely classify the possible pre-monoidal
structures.
All interested are invited
to attend.
Enquiries to Katrina Hibberd email: keh@maths.uq.edu.au