Cohomology of the Lie conformal algebra W(a,b)

The Lie conformal algebra W(a,b) with two parameters a,b is an element of C is a free C[partial derivative]-module generated by L and W satisfying [L lambda L] = (partial derivative + 2 lambda)L, [L lambda W] = (partial derivative + a lambda + b)W and [W lambda W] = 0, which is the semi-direct sums of Virasoro Lie conformal algebra and its nontrivial conformal modules of rank one. In this paper, we determine the basic and reduced cohomology groups of W(a,b) for the case of a is an element of{a <= 2 | a is an element of Q}boolean OR (C - Q) with coefficients in its module. In particular, the low-dimensional basic cohomology groups with trivial coefficients are completely determined.