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2-generation of Chevalley Lie algebras over finite fields

  • Ram Karan Choudhary
  • Harish Kishnani
  • Anupam Singh
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Abstract

In this article, we prove that every split simple Chevalley Lie algebra over a finite field of characteristic p≠ 2 of classical types Bn, Cn, and Dn, and exceptional types G2, F4, E6, E7, and E8, is $2$-generated. Combined with the result of Cantor, Jezernik, and Zozaya for the classical type An [Two-generation of traceless matrices over finite fields, Linear Algebra Appl. (2025)], this establishes $2$-generation for all split simple Chevalley Lie algebras over finite fields of characteristic p≠ 2.

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Cite

BibTeXRIS
BibTeX
@misc{choudhary20262generation,
  title = {{2-generation of Chevalley Lie algebras over finite fields}},
  author = {Ram Karan Choudhary and Harish Kishnani and Anupam Singh},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35537},
  eprint = {2610.35537},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35537},
}
RIS
TY  - UNPB
TI  - 2-generation of Chevalley Lie algebras over finite fields
AU  - Ram Karan Choudhary
AU  - Harish Kishnani
AU  - Anupam Singh
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35537
UR  - https://arxiv.org/abs/2610.35537
AB  - In this article, we prove that every split simple Chevalley Lie algebra over a finite field of characteristic p≠ 2 of classical types B_n, C_n, and D_n, and exceptional types G_2, F_4, E_6, E_7, and E_8, is $2$-generated. Combined with the result of Cantor, Jezernik, and Zozaya for the classical type A_n [Two-generation of traceless matrices over finite fields, Linear Algebra Appl. (2025)], this establishes $2$-generation for all split simple Chevalley Lie algebras over finite fields of characteristic p≠ 2.
ER  -