Lie Conformal Algebras of Planar Galilean Type

Motivated by the Lie structure of the planar Galilean conformal algebra, we construct a class of infinite rank Lie conformal algebras CPG(a,b), where a, b are complex numbers. All their conformal derivations are shown to be inner. The rank-one conformal modules and ℤ-graded free intermediate series modules over CPG(a,b) are completely classified. The parallel results of the finite Lie conformal subalgebra CPG(a,b) of CPG(a,b) are also presented.