Atlas: Trialgebraic deformations of Hopf algebras and a universal symmetry on extended topological quantum field theories by Karl-Georg Schlesinger

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Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories
September 23-28, 2002
Fields Institute
Toronto, ON, Canada

Organizers
George Janelidze, Georgian Academy of Sciences, Bodo Pareigis, University of Munich, Walter Tholen, York University

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Trialgebraic deformations of Hopf algebras and a universal symmetry on extended topological quantum field theories
by
Karl-Georg Schlesinger
Erwin-Schroedinger-Inst., Boltzmanngasse 9, 1090 Vienna, Austria

We study deformations of Hopf algebras which lead to so called trialgebraic structures as they have been suggested by Crane and Frenkel a few years ago as a means to generate certain monoidal bicategories. We give concrete examples of trialgebras constructed by deformation theory and show that trialgebras appear in connection with extended topological quantum field theories (a 2-categorical extension of the concept of an Atiyah functor) in the sense of Kerler and Lyubashenko. We also show that this leads to a universal symmetry structure on extended topological quantum field theories, analogous to the appearance of the Grothendieck-Teichmueller group as a universal symmetry on quasitriangular quasi-Hopf algebras (as studied by Drinfeld).

Date received: May 13, 2002