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.
Type de document :
Pré-publication, Document de travail
19 pages. 2012
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Contributeur : Loïc Foissy <>
Soumis le : lundi 14 mai 2012 - 11:36:07
Dernière modification le : lundi 28 mai 2018 - 16:36:02
Document(s) archivé(s) le : mercredi 15 août 2012 - 02:25:28


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



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



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