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A Duflo Star Product for Poisson Groups
Symmetry, integrability and geometry: methods and applications, Tome 12 (2016) Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $G$ be a finite-dimensional Poisson algebraic, Lie or formal group. We show that the center of the quantization of $G$ provided by an Etingof–Kazhdan functor is isomorphic as an algebra to the Poisson center of the algebra of functions on $G$. This recovers and generalizes Duflo's theorem which gives an isomorphism between the center of the enveloping algebra of a finite-dimensional Lie algebra $\mathfrak{a}$ and the subalgebra of ad-invariant in the symmetric algebra of $\mathfrak{a}$. As our proof relies on Etingof–Kazhdan construction it ultimately depends on the existence of Drinfeld associators, but otherwise it is a fairly simple application of graphical calculus. This shed some lights on Alekseev–Torossian proof of the Kashiwara–Vergne conjecture, and on the relation observed by Bar-Natan–Le–Thurston between the Duflo isomorphism and the Kontsevich integral of the unknot.
Keywords: quantum groups; knot theory; Duflo isomorphism. 
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     author = {Adrien Brochier},
     title = {A {Duflo} {Star} {Product} for {Poisson} {Groups}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a87/}
}
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Adrien Brochier. A Duflo Star Product for Poisson Groups. Symmetry, integrability and geometry: methods and applications, Tome 12 (2016). http://geodesic.mathdoc.fr/item/SIGMA_2016_12_a87/

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