Abstract
In [ 3], Maxim Kontsevich defines explicitely, for each Poisson structure n on the space ℝ d, a star product on ℝ d. If α is linear, i.e. if (ℝ d, α) is the dual of a Lie agebra g, Kontsevich compares his star product with the product defined by S. Gutt in [ 2]. Due to the existence of “wheels” in the Kontsevich's graphs, these two deformations are distinct. If g is nilpotent, the wheels do not appear and the star products coincide. In this Note, we prove this result by computing directly the coefficients of the Kontsevich's star product for this very simple case.
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