Free quadri-algebras and dual quadri-algebras
Combinatorics
2015-04-24 v1
Abstract
We study quadri-algebras and dual quadri-algebras. We describe the free quadri-algebra on one generator as a subobject of the Hopf algebra of permutations FQSym, proving a conjecture due to Aguiar and Loday, using that the operad of quadri-algebras can be obtained from the operad of dendriform algebras by both black and white Manin products. We also give a combinatorial description of free dual quadri-algebras. A notion of quadri-bialgebra is also introduced, with applications to the Hopf algebras FQSym and WQSym.
Keywords
Cite
@article{arxiv.1504.06056,
title = {Free quadri-algebras and dual quadri-algebras},
author = {Loïc Foissy},
journal= {arXiv preprint arXiv:1504.06056},
year = {2015}
}
Comments
19 pages