Deformations of the Lie-Poisson sphere of a compact semisimple Lie algebra

A compact semisimple Lie algebra g induces a Poisson structure pi(S) on the unit sphere S(g*) in g*. We compute the moduli space of Poisson structures on S(g*) around pi(S). This is the first explicit computation of a Poisson moduli space in dimension greater or equal than three around a degenerate (i.e. not symplectic) Poisson structure.