AG Lie-Gruppen: A.-K. Hirmer, FAU: Generalised Kitaev models from Hopf monoids: topological invariance and examples

Generalised Kitaev models from Hopf monoids: topological invariance and
examples – Vortragende: Anna-Katharina Hirmer, FAU Erlangen – Einladender:
Karl-Hermann Neeb

Abstract: Quantum double models were introduced by Kitaev to obtain a
realistic model for a topological quantum computer. They are based on a
directed ribbon graph and a finite-dimensional semisimple Hopf algebra. The
ground state of these models is a topological invariant of a surface, i.e.
only depends on the homeomorphism class of the oriented surface but not the
ribbon graph. Meusburger and Voß generalised part of the construction from
Hopf algebras to pivotal Hopf monoids in symmetric monoidal categories. We
explain the construction of the ground state for involutive Hopf monoids and
show that it is topological invariant. We explicitly describe this
construction for Hopf monoids in Set, Top, Cat and SSet.