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arxiv: 1307.3928 · v3 · pith:OTWMXTKTnew · submitted 2013-07-15 · 🧮 math.CO · hep-th

A combinatorial non-commutative Hopf algebra of graphs

G. H. E. Duchamp , L. Foissy , N. Hoang-Nghia , D. Manchon , A. Tanasa This is my paper
classification 🧮 math.CO hep-th
keywords non-commutativealgebrahopfgraphsscalesassociatedbullcombinatorial
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A non-commutative, planar, Hopf algebra of rooted trees was proposed in L. Foissy, Bull. Sci. Math. 126 (2002) 193-239. In this paper we propose such a non-commutative Hopf algebra for graphs. In order to define a non-commutative product we use a quantum field theoretical (QFT) idea, namely the one of introducing discrete scales on each edge of the graph (which, within the QFT framework, corresponds to energy scales of the associated propagators).

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