A Duflo Star Product for Poisson Groups

  title={A Duflo Star Product for Poisson Groups},
  author={Adrien Brochier},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  • A. Brochier
  • Published 28 April 2016
  • Mathematics
  • Symmetry Integrability and Geometry-methods and Applications
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… 
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