U( h ) -Free Modules over N=2 Super-BMS 3 Algebra

In this paper, a class of non-weight modules over the [Formula: see text] super-[Formula: see text] algebra [Formula: see text] are completely constructed. Denote the Ramond type algebra [Formula: see text] and Neveu-Schwarz type algebra [Formula: see text] by [Formula: see text] and [Formula: see text], respectively. Let [Formula: see text] and [Formula: see text] be the Cartan subalgebras of [Formula: see text] and [Formula: see text], respectively, and let [Formula: see text] be the 3-dimensional subalgebra of [Formula: see text]. These modules over [Formula: see text] are free of rank 1 as modules of the subalgebra [Formula: see text], while these modules over [Formula: see text] are free of rank 2 as modules of the Cartan subalgebra [Formula: see text]. In fact, these modules are isomorphic and reducible. In particular, the non-trivial free [Formula: see text]-modules of rank 1 over [Formula: see text] do not exist. From these modules, we give a complete classification of free [Formula: see text]-modules of rank 1 over [Formula: see text] and free [Formula: see text]-modules of rank 2 over [Formula: see text] separately.