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arXiv · 2205.07509

Classification of simple Harish-Chandra modules over the Ovsienko-Roger superalgebra

Munayim Dilxat·Liangyun Chen·Dong Liu
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Abstract

With the $Ω$-operators for the Virasoro algebra \cite{BF} and the super Virasoro algebra in \cite{CL, CLL}, we get the $Ω$-operators for the Ovsienko-Roger superalgebras in this paper and then use it to classify all simple cuspidal modules for the $\bZ$-graded and $\frac12\bZ$-graded Ovsienko-Roger superalgebras. By this result, we can easily classify all simple Harish-Chandra modules over some related Lie superalgebras, including the $N=1$ BMS$_3$ algebra, the super $W(2,2)$, etc.

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Munayim Dilxat, Liangyun Chen, Dong Liu. 2022-05-16. Classification of simple Harish-Chandra modules over the Ovsienko-Roger superalgebra. https://doi.org/10.1017/prm.2023.20

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