Consider the Poisson structure given by the bivector $\pi:=(x^2+ayz)\partial_y\wedge\partial_z$ on $\mathbb{R}^3$ $(a\neq 0).$ I am interested in the formal Poisson cohomology of this structure.
I believe it is not so easy so any references are welcome or comments that it is out of reach. Note that there are methods for Poisson structure induced by "Classical R-matrices", this structure is unfortunately not of this type.
