$\mathcal{W}(a,b)$ Lie Conformal Algebra and Its Conformal Module of Rank One

For any complex parameters a, b, let [Formula: see text] be the Lie algebra with basis {Li,Hi | i ∈ ℤ} and relations [Li,Lj]=(j-i)Li+j, [Li,Hj]=(a+j+bi)Hi+j and [Hi,Hj]=0. In this paper, we construct the [Formula: see text] conformal algebra for some a, b and its conformal module of rank one.