Simple restricted modules over a new Lie superalgebra extended by the Ovsienko--Roger algebra
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912823253139456 |
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| author | Wang, Jinrong Yue, Xiaoqing |
| author_facet | Wang, Jinrong Yue, Xiaoqing |
| contents | In this paper, we introduce a new infinite-dimensional Lie superalgebra $\mathcal{S}$ called the super extended Ovsienko--Roger algebra. This algebra is obtained by determining the annihilation superalgebra of the Lie conformal superalgebra $S=S_{\bar0}\oplus S_{\bar{1}}$ with $S_{\bar{0}}=\mathbb{C}[\partial]L\oplus\mathbb{C}[\partial]W$, $S_{\bar{1}}=\mathbb{C}[\partial]G$ and non-trivial $λ$-brackets $[L_λL]=(\partial+2λ)L$, $[L_λG]=(\partial+λ)G$, $[L_λW]=[G_λG]=\partial W$. Then we construct a class of simple restricted $\mathcal{S}$-modules, which are induced from simple modules of some finite dimensional solvable Lie superalgebras under certain conditions. Moreover, we obtain the classification of simple generalized Verma modules over $\mathcal{S}$ and we show that the Verma module of $\mathcal{S}$ is always reducible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09277 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simple restricted modules over a new Lie superalgebra extended by the Ovsienko--Roger algebra Wang, Jinrong Yue, Xiaoqing Representation Theory Rings and Algebras 17B05, 17B10, 17B65, 17B68 In this paper, we introduce a new infinite-dimensional Lie superalgebra $\mathcal{S}$ called the super extended Ovsienko--Roger algebra. This algebra is obtained by determining the annihilation superalgebra of the Lie conformal superalgebra $S=S_{\bar0}\oplus S_{\bar{1}}$ with $S_{\bar{0}}=\mathbb{C}[\partial]L\oplus\mathbb{C}[\partial]W$, $S_{\bar{1}}=\mathbb{C}[\partial]G$ and non-trivial $λ$-brackets $[L_λL]=(\partial+2λ)L$, $[L_λG]=(\partial+λ)G$, $[L_λW]=[G_λG]=\partial W$. Then we construct a class of simple restricted $\mathcal{S}$-modules, which are induced from simple modules of some finite dimensional solvable Lie superalgebras under certain conditions. Moreover, we obtain the classification of simple generalized Verma modules over $\mathcal{S}$ and we show that the Verma module of $\mathcal{S}$ is always reducible. |
| title | Simple restricted modules over a new Lie superalgebra extended by the Ovsienko--Roger algebra |
| topic | Representation Theory Rings and Algebras 17B05, 17B10, 17B65, 17B68 |
| url | https://arxiv.org/abs/2601.09277 |