Extensions of modules over a class of Lie conformal algebras $\mathcal{W}(b)$

Abstract

Let $\mathcal{W}(b)$ be a class of free Lie conformal algebras of rank $2$ with $\mathbb{C}[\partial ]$-basis $L,H$ and relations \begin{eqnarray*} [L_λL]=(\partial+2λ)L,\ \ [L_λH]=\big(\partial+(1-b)λ\big)H, \ \ [H_λH]=0, \end{eqnarray*} where $b$ is a nonzero complex number. In this paper, we classify extensions between two finite irreducible conformal modules over the Lie conformal algebras $\mathcal{W}(b)$.

to appear in Journal of Algebra and its Applications