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

15 pages