Realizations of Hopf algebras of graphs by alphabets
Rings and Algebras
2019-05-27 v1
Abstract
We here give polynomial realizations of various Hopf algebras or bialgebras on Feynman graphs, graphs, posets or quasi-posets, that it to say injections of these objects into polynomial algebras generated by an alphabet. The alphabet here considered are totally quasi-ordered. The coproducts are given by doubling the alphabets; a second coproduct is defined by squaring the alphabets, and we obtain cointeracting bialgebras in the commutative case.
Keywords
Cite
@article{arxiv.1905.10203,
title = {Realizations of Hopf algebras of graphs by alphabets},
author = {Loïc Foissy},
journal= {arXiv preprint arXiv:1905.10203},
year = {2019}
}