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arXiv · 2610.35537

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 $p\neq 2$ 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 $p\neq 2$.

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Ram Karan Choudhary, Harish Kishnani, Anupam Singh. 2026-10-26. 2-generation of Chevalley Lie algebras over finite fields. https://arxiv.org/abs/2610.35537

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