Two-generation of traceless matrices over finite fields

Cantor, Omer (author), Jezernik, Urban (author), Zozaya, Andoni (author)

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.

• Language: English
• Keywords: generation, simple Lie algebras, finite fields
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: Str. 1-17
• Numbering: Vol. 713
• PID: 20.500.12556/RUL-169235
• UDC: 512
• ISSN on article: 0024-3795
• DOI: 10.1016/j.laa.2025.02.023
• COBISS.SI-ID: 228710147
• Publication date in RUL: 20.05.2025

Record is a part of a journal

• Title: Linear algebra and its applications
• Shortened title: Linear algebra appl.
• Publisher: Elsevier
• ISSN: 0024-3795
• COBISS.SI-ID: 1119247

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• License: CC BY-NC 4.0, Creative Commons Attribution-NonCommercial 4.0 International
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