We review the method due to Gel’fand and Fuks to show the finite dimensionality of the cohomology ring of the Lie algebra of formal contact vector fields. We apply this method to prove the relative cohomology of it with respect to formal Poisson vector fields is trivial.
Masashi TAKAMURA. "The relative cohomology of formal contact vector fields with respect to formal Poisson vector fields." J. Math. Soc. Japan 60 (1) 117 - 125, January, 2008. https://doi.org/10.2969/jmsj/06010117