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Network Rewriting II: Bi- and Hopf Algebras
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation. (Matematik/tillämpad matematik)ORCID-id: 0000-0001-6140-180X
(engelsk)Manuskript (preprint) (Annet vitenskapelig)
Abstract [en]

Bialgebras and their specialisation Hopf algebras are algebraic structures that challenge traditional mathematical notation, in that they sport two core operations that defy the basic functional paradigm of taking zero or more operands as input and producing one result as output. On the other hand, these peculiarities do not prevent studying them using rewriting techniques, if one works within an appropriate network formalism. This paper restates the traditional axioms as rewriting systems, demonstrating confluence in the case of bialgebras and finding the (infinite) completion in the case of Hopf algebras. A noteworthy minor problem solved along the way is that of constructing a quasi-order with respect to which the rules are compatible.

Emneord [en]
network rewriting, Hopf algebra, bialgebra
HSV kategori
Forskningsprogram
matematik/tillämpad matematik
Identifikatorer
URN: urn:nbn:se:mdh:diva-25102OAI: oai:DiVA.org:mdh-25102DiVA, id: diva2:721600
Merknad

Originally written as a conference contribution, this manuscript prioritises a compact presentation and omits many straightforward calculations.

Tilgjengelig fra: 2014-06-04 Laget: 2014-06-04 Sist oppdatert: 2014-06-24bibliografisk kontrollert

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Hellström, Lars

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