Deformations of the Lie-Poisson sphere of a compact semisimple Lie algebra (Q2877491)

This work gives a perfect classification of Poisson structures on a Lie Poisson sphere that arise from a compact semisimple Lie algebra. It turns out that all such Poisson structures are of the form \(f\pi\), where \(f\) is a Casimir function and \(\pi\) is the standard Lie Poisson form induced from the Lie algebra. Moreover, any two such Poisson structures are isomorphic if and only if the corresponding Casimir functions are gauge equivalent, i.e., only differ by an outer automorphism of the Lie algebra.