Two-generation of traceless matrices over finite fields
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913703766523904 |
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| author | Cantor, Omer Jezernik, Urban Zozaya, Andoni |
| author_facet | Cantor, Omer Jezernik, Urban Zozaya, Andoni |
| contents | We prove that the Lie algebra $\mathfrak{sl}_n(\textbf{F}_q)$ of traceless matrices over a finite field of characteristic $p$ can be generated by $2$ elements with exceptions when $(n, p)$ is $(3, 3)$ or $(4,2)$. In the latter cases, we establish curious identities that obstruct $2$-generation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_11240 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-generation of traceless matrices over finite fields Cantor, Omer Jezernik, Urban Zozaya, Andoni Rings and Algebras 17B05, 17B20 We prove that the Lie algebra $\mathfrak{sl}_n(\textbf{F}_q)$ of traceless matrices over a finite field of characteristic $p$ can be generated by $2$ elements with exceptions when $(n, p)$ is $(3, 3)$ or $(4,2)$. In the latter cases, we establish curious identities that obstruct $2$-generation. |
| title | Two-generation of traceless matrices over finite fields |
| topic | Rings and Algebras 17B05, 17B20 |
| url | https://arxiv.org/abs/2404.11240 |