Resumen de Irreducible modules over the Lie conformal algebra {\mathfrak {B}}(\alpha ,\beta ,p)

Haibo Chen, Yucai Su, Yanyong Hong

• In this paper, we introduce a class of infinite Lie conformal algebras {\mathfrak {B}}(\alpha ,\beta ,p), which are the semi-direct sums of Block type Lie conformal algebra {\mathfrak {B}}(p) and its non-trivial conformal modules of {\mathbb {Z}}-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 {\mathfrak {B}}(\alpha ,\beta ,p) for \alpha ,\beta \in {\mathbb {C}}, p\in {\mathbb {C}}^*. As an application, the classifications of finite irreducible conformal modules over a series of finite Lie conformal algebras {\mathfrak {b}}(n) for {\mathfrak {b}}(n) are given.