Finite irreducible conformal modules over the extended Block type Lie conformal algebra 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 -graded 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∈, p∈*. 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.
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