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Interacting Hopf algebras

Interacting Hopf algebras
Interacting Hopf algebras
We introduce the theory IHR of interacting Hopf algebras, parametrised over a principal ideal domain R. The axioms of IHR are derived using Lack’s approach to composing PROPs: they feature two Hopf algebra and two Frobenius algebra structures on four different monoid–comonoid pairs. This construction is instru- mental in showing that IHR is isomorphic to the PROP of linear relations (i.e. subspaces) over the field of fractions of R
144-184
Bonchi, Filippo
3c53e89d-d280-4911-9938-eb861553d04e
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd
Zanasi, Fabio
5bc03cd7-0fb6-4e14-bae8-8bf0d5d4be38
Bonchi, Filippo
3c53e89d-d280-4911-9938-eb861553d04e
Sobocinski, Pawel
439334ab-2826-447b-9fe5-3928be3fd4fd
Zanasi, Fabio
5bc03cd7-0fb6-4e14-bae8-8bf0d5d4be38

Bonchi, Filippo, Sobocinski, Pawel and Zanasi, Fabio (2017) Interacting Hopf algebras. Journal of Pure and Applied Algebra, 221 (1), 144-184. (doi:10.1016/j.jpaa.2016.06.002).

Record type: Article

Abstract

We introduce the theory IHR of interacting Hopf algebras, parametrised over a principal ideal domain R. The axioms of IHR are derived using Lack’s approach to composing PROPs: they feature two Hopf algebra and two Frobenius algebra structures on four different monoid–comonoid pairs. This construction is instru- mental in showing that IHR is isomorphic to the PROP of linear relations (i.e. subspaces) over the field of fractions of R

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Accepted/In Press date: 8 June 2016
e-pub ahead of print date: 29 June 2016
Published date: January 2017
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Organisations: Electronic & Software Systems
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Identifiers

Local EPrints ID: 406232
URI: http://eprints.soton.ac.uk/id/eprint/406232
DOI: doi:10.1016/j.jpaa.2016.06.002
PURE UUID: 35c41b0b-38a9-4ad9-bf90-118e8da24000

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Date deposited: 10 Mar 2017 10:43
Last modified: 16 Mar 2024 05:05

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Contributors

Author: Filippo Bonchi
Author: Pawel Sobocinski
Author: Fabio Zanasi

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