English

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}
}