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arXiv · 2606.31747

Random generation of the special linear Lie algebra over finite fields

Urban Jezernik·Andoni Zozaya
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Abstract

We prove that the special linear Lie algebra $\mathfrak{sl}_n(\textbf{F}_q)$ over a finite field of characteristic $p$ is generated by two random elements with high probability as $|\mathfrak{sl}_n(\textbf{F}_q)|$ tends to infinity, provided that $(n,p) \neq (3,3), (4,2)$.

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Urban Jezernik, Andoni Zozaya. 2026-06-30. Random generation of the special linear Lie algebra over finite fields. https://arxiv.org/abs/2606.31747

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