### Abstract

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 | United States |

City | New York City |

Period | 5/07/16 → 8/07/16 |

### Fingerprint

### Keywords

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

### Cite this

*Proceedings of the 31st annual ACM/IEEE Symposium on Logic in Computer Science (LICS)*New York, NY. https://doi.org/10.1145/2933575.2934550

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*Proceedings of the 31st annual ACM/IEEE Symposium on Logic in Computer Science (LICS).*New York, NY, 31st Annual ACM/IEEE Symposium on LOGIC IN COMPUTER SCIENCE (LICS2016), New York City, United States, 5/07/16. https://doi.org/10.1145/2933575.2934550

**Interacting Frobenius algebras are Hopf.** / Duncan, Ross; Dunne, Kevin.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - Interacting Frobenius algebras are Hopf

AU - Duncan, Ross

AU - Dunne, Kevin

PY - 2018/12/17

Y1 - 2018/12/17

N2 - 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.

AB - 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.

KW - Frobenius algebras

KW - Hopf algebra

KW - phase group

KW - finite dimensionality

UR - http://lics.rwth-aachen.de/lics16/

UR - http://arxiv.org/abs/1601.04964

U2 - 10.1145/2933575.2934550

DO - 10.1145/2933575.2934550

M3 - Conference contribution book

SN - 9781450343916

BT - Proceedings of the 31st annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

CY - New York, NY

ER -