The Lie conformal algebra of a Block type Lie algebra

Abstract

Let $L$ be a Lie algebra of Block type over $\C$ with basis $\{L_{\alpha,i}\,|\,\alpha,i\in\Z\}$ 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 $\C[\partial]$-basis $\{L_\alpha(w)\,|\,\alpha\in\Z\}$ 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.