Braided Lie algebras and bicovariant differential calculi over coquasitriangular Hopf algebras

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dc.creatorGomez, X.
dc.creatorMajid, S.
dc.date2001-12-28
dc.date2002-01-25
dc.date.accessioned2026-07-07T04:45:34Z
dc.date.available2026-07-07T04:45:34Z
dc.descriptionWe show that if $g_Γ$ is the quantum tangent space (or quantum Lie algebra in the sense of Woronowicz) of a bicovariant first order differential calculus over a coquasitriangular Hopf algebra $(A,r)$, then a certain extension of it is a braided Lie algebra in the category of $A$-comodules. This is used to show that the Woronowicz quantum universal enveloping algebra $U(g_Γ)$ is a bialgebra in the braided category of $A$-comodules. We show that this algebra is quadratic when the calculus is inner. Examples with this unexpected property include finite groups and quantum groups with their standard differential calculi. We also find a quantum Lie functor for coquasitriangular Hopf algebras, which has properties analogous to the classical one. This functor gives trivial results on standard quantum groups $O_q(G)$, but reasonable ones on examples closer to the classical case, such as the cotriangular Jordanian deformations. In addition, we show that split braided Lie algebras define `generalised-Lie algebras' in a different sense of deforming the adjoint representation. We construct these and their enveloping algebras for $O_q(SL_n)$, recovering the Witten algebra for $n=2$.
dc.description42 pages latex; 16 .eps figure files; minor revisions such as simpler presentation of q-relations in example Sec. 5.2
dc.identifierhttps://arxiv.org/abs/math/0112299
dc.identifierhttp://arxiv.org/abs/math/0112299
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62999
dc.subjectQuantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.titleBraided Lie algebras and bicovariant differential calculi over coquasitriangular Hopf algebras
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