A combinatorial non-commutative Hopf algebra of graphs
Combinatorics
2014-06-04 v3 High Energy Physics - Theory
Abstract
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).
Keywords
Cite
@article{arxiv.1307.3928,
title = {A combinatorial non-commutative Hopf algebra of graphs},
author = {G. H. E. Duchamp and L. Foissy and N. Hoang-Nghia and D. Manchon and A. Tanasa},
journal= {arXiv preprint arXiv:1307.3928},
year = {2014}
}
Comments
14 pages, 7 figures; v2 removes the four supplementary pages added by arXiv Latex compiler; v3 introduces a notion of standard labelling for the discrete scales associated to the edges of the graphs. One co-author have been added