Interacting Frobenius Algebras are Hopf

Research output: Contribution to conferenceSpeech

Abstract

Commutative Frobenius algebras play an important role in both TQFT and CQM; in the first case they correspond to 2d TQFTs, while in the second they are non-degenerate observables. I will consider the case of “special” Frobenius algebras, and their associated group of phases. This gives rise to a free construction from the category of abelian groups to the PROP generated by this Frobenius algebra. Of course a theory with only one observable is not very interesting. I will consider how two such PROPs should be combined, and show that if the two algebras (i) jointly form a bialgebra and (ii) their units are “mutually real”; then they jointly form a Hopf algebra. This gives a free model of a pair of strongly complementary observables. I will also consider which unitary maps must exist in such models.
Original languageEnglish
Publication statusPublished - 2015
EventHigher TQFT and categorical quantum mechanics - Erwin Schrödinger Institute, Vienna, Austria
Duration: 19 Oct 201523 Oct 2015
http://www.esi.ac.at/activities/events/2015/higher-topological-quantum-field-theory-and-categorical-quantum-mechanics

Workshop

WorkshopHigher TQFT and categorical quantum mechanics
CountryAustria
CityVienna
Period19/10/1523/10/15
Internet address

Keywords

  • higher topological quantum field theory
  • e Frobenius algebras
  • categorical quantum mechanics
  • abelian groups
  • Hopf algebra
  • bialgebra

Cite this