Abstract
| Original language | English |
|---|---|
| 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) |
|---|---|
| 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
}
Interacting Frobenius algebras are Hopf. / Duncan, Ross; Dunne, Kevin.
Proceedings of the 31st annual ACM/IEEE Symposium on Logic in Computer Science (LICS). New York, NY, 2018.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 -