On the structure of cofree Hopf algebras

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dc.creatorLoday, Jean-Louis
dc.creatorRonco, Maria
dc.date2004-05-17
dc.date2005-03-30
dc.date.accessioned2026-07-07T06:27:45Z
dc.date.available2026-07-07T06:27:45Z
dc.descriptionWe prove an analogue of the Poincare'-Birkhoff-Witt theorem and of the Cartier-Milnor-Moore theorem for non-cocommutative Hopf algebras. The primitive part of a cofree Hopf algebra is a B-infini-algebra. We construct a universal enveloping functor U2 from B-infini-algebras to 2-associative algebras, i.e. algebras equipped with two associative operations. We show that any cofree Hopf algebra H is of the form U2(Prim H). We take advantage of the simple description of the free 2as-algebra in terms of planar trees to unravel the structure of the operad B-infini.
dc.descriptionMinor modifications
dc.identifierhttps://arxiv.org/abs/math/0405330
dc.identifierhttp://arxiv.org/abs/math/0405330
dc.identifierJ. reine angew. Math. 592 (2006), 123--155.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97503
dc.subjectQuantum Algebra
dc.subjectAlgebraic Topology
dc.subject16A24; 16W30; 17A30; 18D50; 81R60
dc.titleOn the structure of cofree Hopf algebras
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