  We define Lie algebra cohomology associated with the half-Dirac operators for
representations of rational Cherednik algebras and show that it has property
described in the Casselman-Osborne Theorem by establishing a version of the
Vogan's conjecture for the half-Dirac operators. Moreover, we study the
relationship between Lie algebra cohomology and Dirac cohomology in analogy of
the representations for semisimple Lie algebras.
