Classification of finite irreducible conformal modules over some Lie conformal algebras related to the Virasoro conformal algebra

摘要

In this paper, we classify all finite irreducible conformal modules over a class of Lie conformal algebras W (b) with b is an element of C related to theVirasoro conformal algebra. Explicitly, any finite irreducible conformal module over W (b) is proved to be isomorphic to M-Delta,M-alpha,M-beta with Delta not equal 0 or beta, 0 if beta = 0, or M-Delta,M-alpha with Delta not equal 0 if b not equal 0. As a byproduct, all finite irreducible conformal modules over the Heisenberg-Virasoro conformal algebra and the W(2, 2) Lie conformal algebra are classified. Finally, the same thing is done for the Schrodinger-Virasoro conformal algebra. Published by AIP Publishing.