Speaker
Prof.
Catherine Meusburger
(Universität Erlangen)
Description
We explain how the concept of a lattice gauge theory with values in a group can be generalised to a gauge theory with values in a Hopf algebra on a graph embedded into a surface. We give an axiomatic description of Hopf algebra gauge theories and show that they include the quantum algebra of observables obtained by the combinatorial quantisation of Chern-Simons theory. We relate Hopf algebra gauge theories to lattice models from condensed matter physics. More specifically, we show that Kitaev's lattice model for a finite-dimensional semisimple Hopf algebra H is equivalent to a Hopf algebra gauge theory for its Drinfeld double D(H).
