Simple modules of the planar Galilean conformal algebra from tensor products

Abstract: This paper is devoted to constructing simple modules of the planar Galilean conformal algebra. We study the tensor products of finitely many simple $\mathcal{U}(\mathcal{H})$-free modules with an arbitrary simple restricted module, where $\mathcal{H}$ is the Cartan subalgebra. We establish necessary and sufficient conditions for simplicity and determine the corresponding isomorphism classes.