On simple restricted modules of Hamiltonian superalgebras with $p$-characters of height 0
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912532837433344 |
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| author | Zhang, Jingyi Chen, Liangyun |
| author_facet | Zhang, Jingyi Chen, Liangyun |
| contents | Let $H(2,1;\underline{t})$ be Hamiltonian superalgebras over $\mathbb{F}$, an algebraically closed field of prime characteristic $p>3$, which are non-restricted simple Lie superalgebras, generally. In this paper, we study generalized $χ$-reduced simple modules over $H(2,1;\underline{t})$. We proved that all generalized $χ$-reduced Kac modules of $H(2,1;\underline{t})$ are simple with $p$-characters $χ$ of height 0. Additionally, the isomorphism classes of these simple $H(2,1;\underline{t})$-modules are classified and their dimensions are determined. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On simple restricted modules of Hamiltonian superalgebras with $p$-characters of height 0 Zhang, Jingyi Chen, Liangyun Representation Theory Rings and Algebras Let $H(2,1;\underline{t})$ be Hamiltonian superalgebras over $\mathbb{F}$, an algebraically closed field of prime characteristic $p>3$, which are non-restricted simple Lie superalgebras, generally. In this paper, we study generalized $χ$-reduced simple modules over $H(2,1;\underline{t})$. We proved that all generalized $χ$-reduced Kac modules of $H(2,1;\underline{t})$ are simple with $p$-characters $χ$ of height 0. Additionally, the isomorphism classes of these simple $H(2,1;\underline{t})$-modules are classified and their dimensions are determined. |
| title | On simple restricted modules of Hamiltonian superalgebras with $p$-characters of height 0 |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2508.08329 |