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Conference Papers Year : 2020

Realizations of Hopf algebras of graphs by alphabets

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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Dates and versions

hal-02137423 , version 1 (23-05-2019)

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Loïc Foissy. Realizations of Hopf algebras of graphs by alphabets. CARMA Conference (Algebraic Combinatorics, Resurgence, Moulds and Applications), Jun 2017, Luminy, France. ⟨10.4171/204-1/5⟩. ⟨hal-02137423⟩
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