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A class of non-weight modules over the super-BMS$_3$ algebra (1911.09651v5)

Published 20 Nov 2019 in math.RT

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 $\S0$ is %equivalent to the category of free $U(\mathfrak{T})$-modules of rank $2$ over %$\S{\frac{1}{2}}$.

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