| Title: | Two-generation of traceless matrices over finite fields |
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| Authors: | ID Cantor, Omer (Author)
ID Jezernik, Urban (Author)
ID Zozaya, Andoni (Author) |
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| Files: |  PDF - Presentation file, download (665,11 KB)
MD5: 1042A02B577233C7DA8B94D784590974
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0024379525000862
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | 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. |
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| Keywords: | generation, simple Lie algebras, finite fields |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.05.2025 |
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| Year of publishing: | 2025 |
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| Number of pages: | str. 1-17 |
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| Numbering: | Vol. 713 |
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| PID: | 20.500.12556/DiRROS-23896  |
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| UDC: | 512 |
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| ISSN on article: | 0024-3795 |
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| DOI: | 10.1016/j.laa.2025.02.023 |
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| COBISS.SI-ID: | 228710147 |
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| Note: |
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| Publication date in DiRROS: | 20.10.2025 |
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| Views: | 211 |
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| Downloads: | 108 |
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| Metadata: |    |
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