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

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 %${\S }^{\frac{1}{2}}$.

arXiv admin note: text overlap with arXiv:1906.07129 by other authors

References in corpus (1)

• On non-weight representations of the $N=2$ superconformal algebras

Cited by in corpus (1)

• A family of simple non-weight modules over the twisted $N=2$ superconformal algebra