A deformation of the \(*\)-product of Gutt on a reductive Lie algebra (Q689448)

The author defines a family of star products on \(\mathbb{R}^ n\) which can be considered as deformation of the star product introduced by \textit{S. Gutt} in Lett. Math. Phys. 7, 249-258 (1983; Zbl 0522.58019) for the polynomial functions on \(\mathbb{R}^ n\). Here \(\mathbb{R}^ n\) is considered as abelian Lie algebra. A relation of the star product to the exponential of the Laplacian is given. The star product can be extended from the polynomial functions to the concentrated Gaussian on \(\mathbb{R}^ n\). Generalization to other Lie algebras are discussed.