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Network Rewriting II: Bi- and Hopf Algebras

Author Lars Hellström

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Lars Hellström

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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) https://doi.org/10.4230/LIPIcs.RTA.2015.194

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.

Subject Classification

Keywords
  • confluence
  • network
  • PROP
  • Hopf algebra

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References

  1. George M. Bergman. The diamond lemma for ring theory. Adv. in Math., 29(2):178-218, 1978. Google Scholar
  2. Masahito Hasegawa. Models of sharing graphs. CPHC/BCS Distinguished Dissertations. Springer-Verlag London, Ltd., London, 1999. A categorical semantics of let and letrec, Dissertation, University of Edinburgh, Edinburgh. Google Scholar
  3. Lars Hellström. Network Rewriting I: The Foundation. ArXiv e-prints, 2012. arXiv:1204.2421 [math.RA]. Google Scholar
  4. Lars Hellström. Critical pairs in network rewriting. In Takahito Aoto and Delia Kesner, editors, IWC 2014, 3rd International Workshop on Confluence, pages 9-13, 2014. URL: http://www.nue.riec.tohoku.ac.jp/iwc2014/iwc2014.pdf.
  5. S. A. Joni and G.-C. Rota. Coalgebras and bialgebras in combinatorics. Stud. Appl. Math., 61(2):93-139, 1979. Google Scholar
  6. Yves Lafont. Towards an algebraic theory of Boolean circuits. J. Pure Appl. Algebra, 184(2-3):257-310, 2003. Google Scholar
  7. Shahn Majid. Cross products by braided groups and bosonization. J. Algebra, 163(1):165-190, 1994. Google Scholar
  8. Samuel Mimram. Computing critical pairs in 2-dimensional rewriting systems. In RTA 2010: Proceedings of the 21st International Conference on Rewriting Techniques and Applications, volume 6 of LIPIcs. Leibniz Int. Proc. Inform., pages 227-241. Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2010. Google Scholar
  9. Roger Penrose. Applications of negative dimensional tensors. In Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969), pages 221-244. Academic Press, London, 1971. Google Scholar
  10. Moss E. Sweedler. Hopf algebras. Mathematics Lecture Note Series. W. A. Benjamin, Inc., New York, 1969. Google Scholar
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