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Network Rewriting II: Bi- and Hopf Algebras
Mälardalen University, School of Education, Culture and Communication. (Matematik/tillämpad matematik)ORCID iD: 0000-0001-6140-180X
(English)Manuscript (preprint) (Other academic)
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.

Keyword [en]
network rewriting, Hopf algebra, bialgebra
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
URN: urn:nbn:se:mdh:diva-25102OAI: diva2:721600

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

Available from: 2014-06-04 Created: 2014-06-04 Last updated: 2014-06-24Bibliographically approved

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Hellström, Lars
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