Interacting Frobenius Algebras are Hopf

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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


WorkshopHigher TQFT and categorical quantum mechanics
Internet address


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

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