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DOI: 10.4230/LIPIcs.RTA.2015.194

Network Rewriting II: Bi- and Hopf Algebras

Authors: Lars Hellström

Published in: LIPIcs, Volume 36, 26th International Conference on Rewriting Techniques and Applications (RTA 2015)

Abstract

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.

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Lars Hellström. Network Rewriting II: Bi- and Hopf Algebras. In 26th International Conference on Rewriting Techniques and Applications (RTA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 36, pp. 194-208, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{hellstrom:LIPIcs.RTA.2015.194,
  author =	{Hellstr\"{o}m, Lars},
  title =	{{Network Rewriting II: Bi- and Hopf Algebras}},
  booktitle =	{26th International Conference on Rewriting Techniques and Applications (RTA 2015)},
  pages =	{194--208},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-85-9},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{36},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2015.194},
  URN =		{urn:nbn:de:0030-drops-51975},
  doi =		{10.4230/LIPIcs.RTA.2015.194},
  annote =	{Keywords: confluence, network, PROP, Hopf algebra}
}

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Network Rewriting II: Bi- and Hopf Algebras

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