PIRSA:17080011

Video URL

https://pirsa.org/17080011

Frobenius algebras, Hopf algebras and 3-categories

Reutter, D. (2017). Frobenius algebras, Hopf algebras and 3-categories. Perimeter Institute for Theoretical Physics. https://pirsa.org/17080011

Reutter, David. Frobenius algebras, Hopf algebras and 3-categories. Perimeter Institute for Theoretical Physics, Aug. 03, 2017, https://pirsa.org/17080011 

          @misc{ scivideos_PIRSA:17080011,
            doi = {10.48660/17080011},
            url = {https://pirsa.org/17080011},
            author = {Reutter, David},
            keywords = {Quantum Foundations, Quantum Information},
            language = {en},
            title = {Frobenius algebras, Hopf algebras and 3-categories},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2017},
            month = {aug},
            note = {PIRSA:17080011 see, \url{https://scivideos.org/pirsa/17080011}}
          }

David Reutter Universität Hamburg

Talk numberPIRSA:17080011
DOI10.48660/17080011
Source RepositoryPIRSA
Collection
Talk Type Conference
Subject

Abstract

It is well known that commutative Frobenius algebras can be represented as topological surfaces, using the graphical calculus of dualizable objects in monoidal 2-categories. We build on related ideas to show that the interacting Frobenius algebras of Duncan and Dunne, which have a Hopf algebra structure, arise naturally in a similar way, by requiring a single 3-morphism in a 3-category to be invertible. We show that this gives a purely geometrical proof of Mueger's version of Tannakian reconstruction of Hopf algebras from fusion categories equipped with a fibre functor. We also relate our results to the theory of lattice code surgery.