The Lie conformal algebra of a Block type Lie algebra

Let $L$ be a Lie algebra of Block type over $\text{C}$ with basis $\{L_{\alpha ,i}\mathrm{\mid }\alpha ,i\in \mathbb{Z}\}$ and brackets $[L_{\alpha ,i},L_{\beta ,j}]=(\beta (i+1)-\alpha (j+1))L_{\alpha +\beta ,i+j}$. In this paper, we shall construct a formal distribution Lie algebra of $L$. Then we decide its conformal algebra $B$ with $\text{C}[\mathrm{\partial }]$-basis $\{L_{\alpha }(w)\mathrm{\mid }\alpha \in \mathbb{Z}\}$ and $\lambda$-brackets $[L_\alpha(w)\lambda L\beta(w)]=(\alpha\partial+(\alpha+\beta)\lambda)L_{\alpha+\beta}(w)$. Finally, we give a classification of free intermediate series $B$-modules.