Classification of finite irreducible conformal modules over a class of Lie conformal algebras of Block type

Abstract

We classify finite irreducible conformal modules over a class of infinite Lie conformal algebras ${\frak {B}}(p)$ of Block type, where $p$ is a nonzero complex number. In particular, we obtain that a finite irreducible conformal module over ${\frak {B}}(p)$ may be a nontrivial extension of a finite conformal module over ${\frak {Vir}}$ if $p=-1$, where ${\frak {Vir}}$ is a Virasoro conformal subalgebra of ${\frak {B}}(p)$. As a byproduct, we also obtain the classification of finite irreducible conformal modules over a series of finite Lie conformal algebras ${\frak b}(n)$ for $n\ge1$.