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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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/articles/10.1142/S1793744212400038/ DO - 10.1142/S1793744212400038 LA - en ID - CML_2012__4_1_A4_0 ER -
%0 Journal Article %A Manchon, Dominique %T On bialgebras and Hopf algebras of oriented graphs %J Confluentes Mathematici %D 2012 %V 4 %N 1 %I World Scientific Publishing Co Pte Ltd %U http://geodesic.mathdoc.fr/articles/10.1142/S1793744212400038/ %R 10.1142/S1793744212400038 %G en %F CML_2012__4_1_A4_0
Manchon, Dominique. On bialgebras and Hopf algebras of oriented graphs. Confluentes Mathematici, Tome 4 (2012) no. 1. doi: 10.1142/S1793744212400038
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