Integrability of infinitesimal automorphisms of linear Poisson manifolds (Q1908716)

The author states that in the linear Poisson manifold, \(\text{sl} (2,\mathbb{R})^*\) with its natural Poisson tensor, any locally Hamiltonian vector field is a global one, this is, it is integrable, it is the Hamiltonian vector field associated to a differentiable function. This is interesting because it constitutes an example of the study of Poisson cohomology of a nonregular Poisson manifold, this is a manifold with a Poisson vector of nonconstant rank. The proof is only sketched.