Natural endomorphisms of shuffle algebras

Abstract : We focus in this text on the adaptation to the study of shuffles of the main combinatorial tool in the theory of free Lie algebras, namely the existence of a universal algebra of endomorphisms for tensor and other cocommutative Hopf algebras: the family of Solomon's descent algebras of type A. We show that there exists similarly a natural endomorphism algebra for commutative shuffle algebras, which is a natural extension of the Malvenuto-Reutenauer Hopf algebra of permutations, or algebra of free quasi-symmetric functions. We study this new algebra for its own, establish freeness properties, study its generators, bases, and also feature its relations to the internal structure of shuffle algebras.
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Pré-publication, Document de travail
19 pages. 2012
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https://hal.archives-ouvertes.fr/hal-00696965
Contributeur : Loïc Foissy <>
Soumis le : lundi 14 mai 2012 - 11:36:07
Dernière modification le : mercredi 23 mars 2016 - 01:00:41
Document(s) archivé(s) le : mercredi 15 août 2012 - 02:25:28

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EndoShuffle.pdf
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  • HAL Id : hal-00696965, version 1
  • ARXIV : 1205.2986

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Loïc Foissy, Frédéric Patras. Natural endomorphisms of shuffle algebras. 19 pages. 2012. <hal-00696965>

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