W- algebras and Duflo Isomorphism

الأصل · EN

We prove that when Kontsevich's deformation quantization is applied on weight homogeneous Poisson structures, the operators in the - product formula are weight homogeneous. We then consider the linear Poisson case X=g for a semi simple Lie algebra g. As an application we provide an isomorphism between the Cattaneo-Felder-Torossian reduction algebra H⁰(g,m,χ) and the W- algebra (U(g)/U(g)mχ)ᵐ. We also show that in the W- algebra setting, (S(g)/S(g)mχ)ᵐ is polynomial. Finally, we compute generators of H⁰(g,m,χ) as a deformation of (S(g)/S(g)mχ)ᵐ.