U(h)-free modules over the topological N = 2 super-BMS3 algebra

In this paper, a class of non-weight modules over the topological N = 2 super-BMS3 algebra g are completely constructed. Assume that h̄=CL0⊕CP0⊕CG0⊕CQ0 is the Cartan subalgebra of g and h=CL0⊕CP0 is a two-dimensional subalgebra of h̄. These modules over g are free of rank 2 as modules of the subalgebra h. In fact, these modules are reducible. Moreover, we give a complete classification of free U(h)-modules of rank 2 over g.