Braided-Lie bialgebras

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dc.creatorMajid, S.
dc.date1997-03-03
dc.date.accessioned2026-07-07T09:17:30Z
dc.date.available2026-07-07T09:17:30Z
dc.descriptionWe introduce braided Lie bialgebras as the infinitesimal version of braided groups. They are Lie algebras and Lie coalgebras with the coboundary of the Lie cobracket an infinitesimal braiding. We provide theorems of transmutation, Lie biproduct, bosonisation and double-bosonisation relating braided Lie bialgebras to usual Lie bialgebras. Among the results, the kernel of any split projection of Lie bialgebras is a braided-Lie bialgebra. The Kirillov-Kostant Lie cobracket provides a natural braided-Lie bialgebra on any complex simple Lie algebra $g$, as the transmutation of the Drinfeld-Sklyanin Lie cobracket. Other nontrivial braided-Lie bialgebras are associated to the inductive construction of simple Lie bialgebras along the $C$ and exceptional series.
dc.description32 pages LATEX, no figures
dc.identifierhttps://arxiv.org/abs/q-alg/9703004
dc.identifierhttp://arxiv.org/abs/q-alg/9703004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/153689
dc.subjectQuantum Algebra
dc.titleBraided-Lie bialgebras
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