Mapping class group actions in Kitaev's quantum double models and their generalisations

02.04.2024 15:30 – 16:30

Quantum double models play an important role in topological quantum computing and topological quantum field theory (TQFT). They assign to an oriented surface with an embedded graph and a finite-dimensional semisimple Hopf algebra a vector space, the ground state, that is independent of the graph. It is the vector space the Turaev-Viro TQFT assigns to the surface and carries an action of the mapping class group.

We give a simple description of mapping class group actions in the quantum double model with and without boundary. We then show how the quantum double model and the associated mapping class group actions can be generalised to involutive Hopf monoids in complete and cocomplete symmetric monoidal categories. This allows for interesting examples that cannot be treated in the framework of TQFTs.

This is joint work with Thomas Voß and Anna-Katharina Hirmer.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-07, Séminaire "Groupes de Lie et espaces de modules"

entrée libre