eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-06-18
194
208
10.4230/LIPIcs.RTA.2015.194
article
Network Rewriting II: Bi- and Hopf Algebras
Hellström, Lars
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol036-rta2015/LIPIcs.RTA.2015.194/LIPIcs.RTA.2015.194.pdf
confluence
network
PROP
Hopf algebra