Abstract
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 language | English |
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Title of host publication | Proceedings of the 31st annual ACM/IEEE Symposium on Logic in Computer Science (LICS) |
Place of Publication | New York, NY |
Number of pages | 10 |
DOIs | |
Publication status | Published - 17 Dec 2018 |
Event | 31st Annual ACM/IEEE Symposium on LOGIC IN COMPUTER SCIENCE (LICS2016): LICS2016 - New York City, United States Duration: 5 Jul 2016 → 8 Jul 2016 |
Conference
Conference | 31st Annual ACM/IEEE Symposium on LOGIC IN COMPUTER SCIENCE (LICS2016) |
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Country/Territory | United States |
City | New York City |
Period | 5/07/16 → 8/07/16 |
Keywords
- Frobenius algebras
- Hopf algebra
- phase group
- finite dimensionality