A Duflo Star Product for Poisson Groups
Abstract
Let G be a finitedimensional Poisson algebraic, Lie or formal group. We show that the center of the quantization of G provided by an EtingofKazhdan 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 finitedimensional Lie algebra a and the subalgebra of adinvariant in the symmetric algebra of a. As our proof relies on EtingofKazhdan 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 AlekseevTorossian proof of the KashiwaraVergne conjecture, and on the relation observed by BarNatanLeThurston between the Duflo isomorphism and the Kontsevich integral of the unknot.
 Publication:

SIGMA
 Pub Date:
 September 2016
 DOI:
 10.3842/SIGMA.2016.088
 arXiv:
 arXiv:1604.08450
 Bibcode:
 2016SIGMA..12..088B
 Keywords:

 quantum groups;
 knot theory;
 Duflo isomorphism;
 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory
 EPrint:
 SIGMA 12 (2016), 088, 12 pages