A convergent star product for linear Poisson structures

An explicit star product ⋆ Γ on the dual of a general Lie algebra equipped with the linear Poisson bracket is constructed. An equivalence operator between this star product and the Kontsevich star product in [K1] is given and diverse properties of the star product ⋆ Γ are studied. It is also proved that the star product ⋆ α Γ provides a convergent deformation quantization in the sense of Rieffel [R1].