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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2604.18369 |
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Table des matières:
- 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.