Catherine Meusburger (U Erlangen): Kitaev lattice models as a Hopf algebra gauge theory


We generalise the notion of a lattice gauge theory with values in a
group to Hopf algebra valued lattice gauge theories and show that a
Kitaev lattice model for a finite-dimensional semisimple Hopf algebra H
is equivalent to a Hopf algebra gauge theory for the Drinfeld double
D(H). This shows in particular that Kitaev models are a special case of
combinatorial quantisation of Chern-Simons theory introduced by
Alekseev, Grosse, Schomerus und Buffenoir and Roche. This can be viewed
as an analogue of the relation between Turaev-Viro and
Reshetikhin-Turaev TQFTs and explicitly relates Kitaev models to the
quantisation of moduli spaces of flat connections on surfaces.

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March 30, 2017