Finite irreducible conformal modules over the extended Block type Lie conformal algebra $\mathfrak{B}(α,β,p)$

Abstract

In this paper, we introduce a class of infinite Lie conformal algebras B(α, β, p), which are the semi-direct sums of Block type Lie conformal algebra B(p) and its non-trivial conformal modules of Zgraded free intermediate series. The annihilation algebras are a class of infinite-dimensional Lie algebras, which include a lot of interesting subalgebras: Virasoro algebra, Block type Lie algebra, twisted Heisenberg-Virasoro algebra and so on. We give a complete classification of all finite non-trivial irreducible conformal modules of B(α, β, p) for α, β ∈ C, p ∈ C * . As an application, the classifications of finite irreducible conformal modules over a series of finite Lie conformal algebras b(n) for n ≥ 1 are given.