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arXiv · 1905.10203

Realizations of Hopf algebras of graphs by alphabets

Loïc Foissy
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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.

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Loïc Foissy. 2019-05-24. Realizations of Hopf algebras of graphs by alphabets. https://arxiv.org/abs/1905.10203

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