Structure of the Malvenuto-Reutenauer Hopf algebra of permutations (Extended Abstract)

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dc.creatorAguiar, Marcelo
dc.creatorSottile, Frank
dc.date2002-03-11
dc.date2002-03-27
dc.date.accessioned2026-07-07T04:46:58Z
dc.date.available2026-07-07T04:46:58Z
dc.descriptionWe analyze the structure of the Malvenuto-Reutenauer Hopf algebra of permutations in detail. We give explicit formulas for its antipode, prove that it is a cofree coalgebra, determine its primitive elements and its coradical filtration and show that it decomposes as a crossed product over the Hopf algebra of quasi-symmetric functions. We also describe the structure constants of the multiplication as a certain number of facets of the permutahedron. Our results reveal a close relationship between the structure of this Hopf algebra and the weak order on the symmetric groups.
dc.description12 pages, 2 .eps figures. (minor revisions) Extended abstract for Formal Power Series and Algebraic Combinatorics, Melbourne, July 2002
dc.identifierhttps://arxiv.org/abs/math/0203101
dc.identifierhttp://arxiv.org/abs/math/0203101
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63539
dc.subjectCombinatorics
dc.subjectQuantum Algebra
dc.subjectRings and Algebras
dc.subject05E05, 06A11, 16W30
dc.titleStructure of the Malvenuto-Reutenauer Hopf algebra of permutations (Extended Abstract)
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