Simple modules of the planar Galilean conformal algebra from tensor products

TL;DR

This paper constructs and classifies simple modules of the planar Galilean conformal algebra using tensor products, providing criteria for simplicity and identifying isomorphism classes.

Contribution

It introduces a method to build simple modules via tensor products and characterizes their simplicity and classification.

Findings

Established necessary and sufficient conditions for module simplicity

Classified isomorphism classes of the constructed modules

Extended understanding of the module structure of the planar Galilean conformal algebra

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.