On a general approach to the formal cohomology of quadratic Poisson   structures
  We propose a general approach to the formal Poisson cohomology of $r$-matrix induced quadratic structures, we apply this device to compute the cohomology of structure 2 of the Dufour-Haraki classification, and provide complete results also for the cohomology of structure 7. 
Mohsen Masmoudi, Norbert Poncin