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

TL;DR

This paper constructs and classifies a new class of non-weight modules over super-BMS3 algebras, revealing their simplicity conditions and isomorphism criteria, and establishing an equivalence between module categories.

Contribution

It introduces a novel class of non-weight modules over super-BMS3 algebras and characterizes their structure, simplicity, and isomorphism conditions.

Findings

Modules over  are free of rank 1 over the Cartan subalgebra.

Modules over .5 are free of rank 2 over the Cartan subalgebra.

Category of free modules over  is equivalent to that over .5.

Abstract

In the present paper, a class of non-weight modules over the super-BMS$_3$ algebras $\S^{\epsilon}$ ($\epsilon=0$ or $\frac{1}{2}$) are constructed. Assume that $\mathfrak{t}=\C L_0\oplus\C W_0\oplus\C G_0$ and $\mathfrak{T}=\C L_0\oplus\C W_0$ are the Cartan subalgebra (modulo center) of $\S^{0}$ and $\S^{\frac{1}{2}}$, respectively. These modules over $\S^{0}$ when restricted to the $\mathfrak{t}$ are free of rank $1$, while these modules over $\S^{\frac{1}{2}}$ 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 $\S^{\epsilon}$-modules being isomorphic. %Moreover, we see that the category of free $U(\mathfrak{t})$-modules of rank $1$ over $\S^0$ is %equivalent to the category of free $U(\mathfrak{T})$-modules of rank $2$ over %$\S^{\frac{1}{2}}$.