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

The Lie conformal algebra [Formula: see text] with two parameters [Formula: see text] is a free [Formula: see text]-module generated by [Formula: see text] and [Formula: see text] satisfying [Formula: see text] and [Formula: see text], 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 [Formula: see text] for the case of [Formula: see text] with coefficients in its module. In particular, the low-dimensional basic cohomology groups with trivial coefficients are completely determined.