2016-06-01: Kevin Dunne (MSP)

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

Kevin Dunne (MSP)

Interacting Frobenius algebras

Abstract

Practice talk for QPL.

Theories featuring the interaction between a Frobenius algebra and a Hopf algebra have recently appeared in several areas in computer science: concurrent programming, control theory, and quantum computing, among others. Bonchi, Sobocinski, and Zanasi (2014) have shown that, given a suitable distributive law, a pair of Hopf algebras forms two Frobenius algebras. Here we take the opposite approach, and show that interacting Frobenius algebras form Hopf algebras. We generalise (BSZ 2014) by including non-trivial dynamics of the underlying object – the so-called phase group – and investigate the effects of finite dimensionality of the underlying model. We recover the system of Bonchi et al as a subtheory in the prime power dimensional case, but the more general theory does not arise from a distributive law.

2016-06-01 12:00:00 UTC
LT1310