Random generation of the special linear Lie algebra over finite fields

Urban Jezernik; Andoni Zozaya

Random generation of the special linear Lie algebra over finite fields

Rings and Algebras 2026-06-30 v1

Authors: Urban Jezernik , Andoni Zozaya

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 $(n,p) \neq (3,3), (4,2)$ .

Keywords

random generation special linear Lie algebra finite fields generating sets probability

Cite

@article{arxiv.2606.31747,
  title  = {Random generation of the special linear Lie algebra over finite fields},
  author = {Urban Jezernik and Andoni Zozaya},
  journal= {arXiv preprint arXiv:2606.31747},
  year   = {2026}
}