The Lie conformal algebra of a Block type Lie algebra

Abstract

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

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Cited by in corpus (3)

• Loop Virasoro Lie Conformal Algebra
• Central extensions and conformal derivations of a class of Lie conformal algebras
• A new class of Z-graded Lie conformal algebras of infinite rank