2015-10-28: Ross Duncan (MSP)

Tue, 14 Oct 2025 16:51:42 +0000

Ross Duncan (MSP)

Interacting Frobenius Algebras Are Hopf

Abstract

Commutative Frobenius algebras play an important role in both Topological Quantum Field Theory and Categorical Quantum Mechanics; 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.

Slides are here if you want a preview.

2015-10-28 11:00:00 UTC
LT1310