A class of non-weight modules over the super-BMS${}_3$ algebra

In the present paper, a class of non-weight modules over the super-BMS${}_3$ algebras ${\mathrm{\S }}^{ϵ}$ ($ϵ=0$ or $\frac{1}{2}$) are constructed. Assume that $\mathfrak{t}=\text{C}{L}_0\oplus \text{C}{W}_0\oplus \text{C}{G}_0$ and $\mathfrak{T}=\C L_0\oplus\C W_0$aretheCartansubalgebra(modulocenter)of$\S^{0}$and$\S^{\frac{1}{2}}$,respectively\mathrm{.}Thesemodulesover$\S^{0}$ when restricted to the $\mathfrak{t}$ are free of rank $1$, while these modules over ${\mathrm{\S }}^{\frac{1}{2}}$ when restricted to the $\mathfrak{T}$ are free of rank $2$. Then we determine the necessary and sufficient conditions for these modules being simple, as well as determining the necessary and sufficient conditions for two ${\mathrm{\S }}^{ϵ}$-modules being isomorphic. %Moreover, we see that the category of free $U(\mathfrak{t})$-modules of rank $1$ over ${\mathrm{\S }}^0$ is %equivalent to the category of free $U(\mathfrak{T})$-modules of rank $2$ over %${\mathrm{\S }}^{\frac{1}{2}}$.