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

TL;DR

This paper classifies finite irreducible conformal modules over certain infinite Lie conformal algebras of Block type, revealing extensions involving Virasoro modules and also classifying modules over related finite algebras.

Contribution

It provides the first classification of finite irreducible conformal modules over Lie conformal algebras of Block type and related finite algebras.

Findings

Finite irreducible modules over ${rak {B}}(p)$ are classified.

Nontrivial extensions of Virasoro modules occur when p=-1.

Classification of modules over finite Lie conformal algebras ${rak b}(n)$.

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 $n\ge1$.