Simple modules over truncated current Lie algebras of the Witt algebra
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913047980802048 |
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| author | Chang, Hao Hou, Ruiying Hu, Jinxin |
| author_facet | Chang, Hao Hou, Ruiying Hu, Jinxin |
| contents | Let $\Bbbk$ be an algebraically closed field of characteristic $p>3$, and let $W$ denote the $p$-dimensional Witt algebra, the first example of a non-classical simple Lie algebra. For a non-negative integer $\ell$, consider the associated truncated current Lie algebra $W_\ell=W \otimes \Bbbk[t]/(t^{\ell+1})$. In this paper, we first study simple $W_\ell$-modules having $p$-character $χ$ of height at most one, and provide a complete classification of such modules up to isomorphism. We then investigate a family of simple $W_\ell$-modules whose $p$-characters have height greater than one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18369 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simple modules over truncated current Lie algebras of the Witt algebra Chang, Hao Hou, Ruiying Hu, Jinxin Representation Theory 2020:17B50 Let $\Bbbk$ be an algebraically closed field of characteristic $p>3$, and let $W$ denote the $p$-dimensional Witt algebra, the first example of a non-classical simple Lie algebra. For a non-negative integer $\ell$, consider the associated truncated current Lie algebra $W_\ell=W \otimes \Bbbk[t]/(t^{\ell+1})$. In this paper, we first study simple $W_\ell$-modules having $p$-character $χ$ of height at most one, and provide a complete classification of such modules up to isomorphism. We then investigate a family of simple $W_\ell$-modules whose $p$-characters have height greater than one. |
| title | Simple modules over truncated current Lie algebras of the Witt algebra |
| topic | Representation Theory 2020:17B50 |
| url | https://arxiv.org/abs/2604.18369 |