Interacting Frobenius algebras are Hopf

Ross Duncan, Kevin Dunne

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

18 Citations (Scopus)
148 Downloads (Pure)


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.
Original languageEnglish
Title of host publicationProceedings of the 31st annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
Place of PublicationNew York, NY
Number of pages10
Publication statusPublished - 17 Dec 2018
Event31st Annual ACM/IEEE Symposium on LOGIC IN COMPUTER SCIENCE (LICS2016): LICS2016 - New York City, United States
Duration: 5 Jul 20168 Jul 2016


Conference31st Annual ACM/IEEE Symposium on LOGIC IN COMPUTER SCIENCE (LICS2016)
Country/TerritoryUnited States
CityNew York City


  • Frobenius algebras
  • Hopf algebra
  • phase group
  • finite dimensionality


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