We define two coproducts for cycle-free oriented graphs, thus building up two commutative connected graded Hopf algebras, such that one is a comodule-coalgebra on the other, thus generalizing the result obtained in [2] for Hopf algebras of rooted trees.
@article{CML_2012__4_1_A4_0,
author = {Manchon, Dominique},
title = {On bialgebras and {Hopf} algebras of oriented graphs},
journal = {Confluentes Mathematici},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {4},
number = {1},
year = {2012},
doi = {10.1142/S1793744212400038},
language = {en},
url = {http://www.numdam.org/articles/10.1142/S1793744212400038/}
}
TY - JOUR AU - Manchon, Dominique TI - On bialgebras and Hopf algebras of oriented graphs JO - Confluentes Mathematici PY - 2012 VL - 4 IS - 1 PB - World Scientific Publishing Co Pte Ltd UR - http://www.numdam.org/articles/10.1142/S1793744212400038/ DO - 10.1142/S1793744212400038 LA - en ID - CML_2012__4_1_A4_0 ER -
Manchon, Dominique. On bialgebras and Hopf algebras of oriented graphs. Confluentes Mathematici, Tome 4 (2012) no. 1. doi : 10.1142/S1793744212400038. http://www.numdam.org/articles/10.1142/S1793744212400038/
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