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Network Rewriting II: Bi- and Hopf Algebras
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0001-6140-180X
2015 (English)In: Leibniz International Proceedings in Informatics, LIPIcs, Volume 36 / [ed] Maribel Fernández, Dagstuhl, Germany: Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik , 2015, Vol. 36, 194-208 p.Conference paper, Published paper (Refereed)
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 rather than the traditional term 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.

Place, publisher, year, edition, pages
Dagstuhl, Germany: Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik , 2015. Vol. 36, 194-208 p.
Series
Leibniz International Proceedings in Informatics (LIPIcs), ISSN 1868-8969
Keyword [en]
confluence, network, PROP, Hopf algebra, bialgebra, rewriting
National Category
Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-29884DOI: 10.4230/LIPIcs.RTA.2015.194Scopus ID: 2-s2.0-84958953312ISBN: 978-3-939897-85-9 (print)OAI: oai:DiVA.org:mdh-29884DiVA: diva2:881129
Conference
26th International Conference on Rewriting Techniques and Applications (RTA 2015), June 29 to July 1, 2015 - Warsaw, Poland
Available from: 2015-12-09 Created: 2015-12-09 Last updated: 2016-10-11Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf