PIRSA:19110142

Video URL

https://pirsa.org/19110142

Mapping class group actions on Hopf algebra lattice models

Voss, T. (2019). Mapping class group actions on Hopf algebra lattice models. Perimeter Institute for Theoretical Physics. https://pirsa.org/19110142

Voss, Thomas. Mapping class group actions on Hopf algebra lattice models. Perimeter Institute for Theoretical Physics, Nov. 28, 2019, https://pirsa.org/19110142 

          @misc{ scivideos_PIRSA:19110142,
            doi = {10.48660/19110142},
            url = {https://pirsa.org/19110142},
            author = {Voss, Thomas},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Mapping class group actions on Hopf algebra lattice models},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2019},
            month = {nov},
            note = {PIRSA:19110142 see, \url{https://scivideos.org/index.php/pirsa/19110142}}
          }

Thomas Voss University of Erlangen-Nuremberg

Talk numberPIRSA:19110142
DOI10.48660/19110142
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

Hopf algebra lattice models are related to certain topological quantum field theories and give rise to topological invariants of oriented surfaces. Examples are the combinatorial quantisation of Chern-Simons theory and the Kitaev model.
Our main result is the construction of a mapping class group action on these models, formulated under weaker assumptions than the associated topological quantum field theories, namely for pivotal Hopf algebras in symmetric monoidal categories. This description also yields new structures for semisimple finite-dimensional Hopf algebras. The action of the mapping class group is defined in terms of simple graph transformations and allows one to compute quantum Dehn twists explicitly.