On simple restricted modules of Hamiltonian superalgebras with $p$-characters of height 0

Jingyi Zhang; Liangyun Chen

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arXiv · 2508.08329

On simple restricted modules of Hamiltonian superalgebras with $p$-characters of height 0

Jingyi Zhang·Liangyun Chen

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Abstract

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.

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BibTeX RIS

Jingyi Zhang, Liangyun Chen. 2025-08-10. On simple restricted modules of Hamiltonian superalgebras with $p$-characters of height 0. https://arxiv.org/abs/2508.08329

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