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Gauge Twists and Hennings TQFT's
by
Thomas Kerler
The Ohio State University
Coauthors: Qi Chen
The notion of a gauge twist of the co-algebra structure of a (strict) quasi-triangular Hopf algebra goes back to Drinfeld (1987). Such Hopf algebras also serve to construct TQFT's by extension of the Hennings calculus. This naturally raises the questions how TQFT's constructed from gauge twist equivalent Hopf algebra are related.
We show that these TQFT's are isomorphic and explicitly construct the natural isomorphism of TQFT-functors from the gauge twist tensor. A useful example arises from the observation that the double of the quantum-sl_2 Borel subalgbera is gauge twist equivalent to the tensor product of quantum-sl_2 and a copy of the Cartan subalgebra. We apply this in our forthcoming paper to prove integrality of associated quantum invariants.
Date received: April 14, 2011
Copyright © 2011 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbcc-11.