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Macquarie University  Department of Mathematics

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Categories in Algebra, Geometry and Mathematical Physics

Conference in honour of Ross Street's sixtieth birthday

July 11-16 2005, Macquarie University, Sydney

Wed, 13 July:  11:30 - 12:10

On modular categories and group actions on braided tensor categories
Mueger, Michael (Radboud University, Nijmegen)

Modular categories as defined by Turaev some ten years ago are a fairly special but also extremely interesting class of braided tensor categories with connections to quantum and loop groups, number theory, and topological and conformal quantum field theory. After recalling the definition and some more or less well-known results I will discuss two open conjectures concerning modular categories: the congruence subgroup conjecture and the modular embedding conjecture.

I will then discuss actions of discrete groups on (more general) braided tensor categories and their bearing on the conjectures mentioned above. This is work in progress and I will summarize the state of affairs.

Typeset PDF of this abstract.