U ( h ) -free modules over the super-Galilean conformal algebras

Abstract

In this paper, we study non-weight modules over the super-Galilean conformal algebra. We construct and classify [Formula: see text]-free modules of rank 1 over the Ramond-type algebra and [Formula: see text]-free modules of rank 2 over the Neveu–Schwarz-type algebra, where [Formula: see text] is a subalgebra of the Ramond-type algebra and [Formula: see text] is the Cartan algebra of the Neveu–Schwarz-type algebra. We find that these modules are reducible and isomorphic.