Quantization of Poisson-Hopf stacks associated with group Lie bialgebras

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dc.creatorHalbout, Gilles
dc.creatorTang, Xiang
dc.date2007-03-12
dc.date.accessioned2026-07-07T07:51:41Z
dc.date.available2026-07-07T07:51:41Z
dc.descriptionLet $G$ be a Poisson Lie group and $\g$ its Lie bialgebra. Suppose that $\g$ is a group Lie bialgebra. This means that there is an action of a discrete group $Γ$ on $G$ deforming the Poisson structure into coboundary equivalent ones. Starting from this we construct a non-trivial stack of Hopf-Poisson algebras and prove the existence of associated deformation quantizations. This non-trivial stack is a stack of functions on the formal Poisson group, dual of the starting $Γ$ Poisson-Lie group. To quantize this non-trivial stack we use quantization of a $Γ$ Lie bialgebra which is the infinitesimal of a $Γ$ Poisson-Lie group (cf \cite{MS} for simple Lie groups and $Γ$ a covering of the Weyl group and \cite{EH} for quantization in the general case).
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/math/0703359
dc.identifierhttp://arxiv.org/abs/math/0703359
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125606
dc.subjectQuantum Algebra
dc.subjectSymplectic Geometry
dc.subject17B37, 58H05
dc.titleQuantization of Poisson-Hopf stacks associated with group Lie bialgebras
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