Generalized bialgebras and triples of operads

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dc.creatorLoday, Jean-Louis
dc.date2006-11-28
dc.date2008-12-16
dc.date.accessioned2026-07-07T12:12:58Z
dc.date.available2026-07-07T12:12:58Z
dc.descriptionWe introduce the notion of generalized bialgebra, which includes the classical notion of bialgebra (Hopf algebra) and many others. We prove that, under some mild conditions, a connected generalized bialgebra is completely determined by its primitive part. This structure theorem extends the classical Poincaré-Birkhoff-Witt theorem and the Cartier-Milnor-Moore theorem, valid for cocommutative bialgebras, to a large class of generalized bialgebras. Technically we work in the theory of operads which permits us to give a conceptual proof of our main theorem. It unifies several results, generalizing PBW and CMM, scattered in the literature. We treat many explicit examples and suggest a few conjectures.
dc.descriptionSlight modification of the quotient triple proposition (3.1.1). Typos corrected. 110 pages
dc.identifierhttps://arxiv.org/abs/math/0611885
dc.identifierhttp://arxiv.org/abs/math/0611885
dc.identifierAste'risque 320 (2008), vi+114 pp.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210723
dc.subjectQuantum Algebra
dc.subjectCombinatorics
dc.subjectCategory Theory
dc.subject16A24, 16W30, 17A30, 18D50, 81R60
dc.titleGeneralized bialgebras and triples of operads
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