Shuffle bialgebras

María Ronco[1]

  • [1] CIMFAV, Fac. de Ciencias Universidad de Valparaíso Avda. Gran Bretaña 1091 Valparaíso (Chile)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 3, page 799-850
  • ISSN: 0373-0956

Abstract

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The goal of our work is to study the spaces of primitive elements of some combinatorial Hopf algebras, whose underlying vector spaces admit linear basis labelled by subsets of the set of maps between finite sets. In order to deal with these objects we introduce the notion of shuffle algebras, which are coloured algebras where composition is not always defined. We define bialgebras in this framework and compute the subpaces of primitive elements associated to them. These spaces of primitive elements have natural structure of some type of coloured algebras, which we describe in terms of generators and relations.

How to cite

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Ronco, María. "Shuffle bialgebras." Annales de l’institut Fourier 61.3 (2011): 799-850. <http://eudml.org/doc/219729>.

@article{Ronco2011,
abstract = {The goal of our work is to study the spaces of primitive elements of some combinatorial Hopf algebras, whose underlying vector spaces admit linear basis labelled by subsets of the set of maps between finite sets. In order to deal with these objects we introduce the notion of shuffle algebras, which are coloured algebras where composition is not always defined. We define bialgebras in this framework and compute the subpaces of primitive elements associated to them. These spaces of primitive elements have natural structure of some type of coloured algebras, which we describe in terms of generators and relations.},
affiliation = {CIMFAV, Fac. de Ciencias Universidad de Valparaíso Avda. Gran Bretaña 1091 Valparaíso (Chile)},
author = {Ronco, María},
journal = {Annales de l’institut Fourier},
keywords = {Bialgebra; planar rooted trees; shuffles; combinatorial Hopf algebras; bialgebras},
language = {eng},
number = {3},
pages = {799-850},
publisher = {Association des Annales de l’institut Fourier},
title = {Shuffle bialgebras},
url = {http://eudml.org/doc/219729},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Ronco, María
TI - Shuffle bialgebras
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 3
SP - 799
EP - 850
AB - The goal of our work is to study the spaces of primitive elements of some combinatorial Hopf algebras, whose underlying vector spaces admit linear basis labelled by subsets of the set of maps between finite sets. In order to deal with these objects we introduce the notion of shuffle algebras, which are coloured algebras where composition is not always defined. We define bialgebras in this framework and compute the subpaces of primitive elements associated to them. These spaces of primitive elements have natural structure of some type of coloured algebras, which we describe in terms of generators and relations.
LA - eng
KW - Bialgebra; planar rooted trees; shuffles; combinatorial Hopf algebras; bialgebras
UR - http://eudml.org/doc/219729
ER -

References

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