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.