Lie conformal algebras related to Galilean conformal algebras

Let R(a, b) be a Lie conformal algebra related to Galilean conformal algebras, where a, b are complex numbers. All the conformal derivations of R(a, b) are shown to be inner. The rank one conformal modules and Z-graded free intermediate series modules over R(a, b) are completely classified. The corresponding results of the finite conformal subalgebra of R(a, b) are also obtained as byproducts.