Classification of simple Harish-Chandra modules over the Ovsienko-Roger superalgebra
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866916155995717632 |
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| author | Dilxat, Munayim Chen, Liangyun Liu, Dong |
| author_facet | Dilxat, Munayim Chen, Liangyun Liu, Dong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_07509 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Classification of simple Harish-Chandra modules over the Ovsienko-Roger superalgebra Dilxat, Munayim Chen, Liangyun Liu, Dong Representation Theory Mathematical Physics Rings and Algebras 17B10, 17B20, 17B65, 17B66, 17B68 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. |
| title | Classification of simple Harish-Chandra modules over the Ovsienko-Roger superalgebra |
| topic | Representation Theory Mathematical Physics Rings and Algebras 17B10, 17B20, 17B65, 17B66, 17B68 |
| url | https://arxiv.org/abs/2205.07509 |