Two-generation of traceless matrices over finite fields
Omer Cantor, Urban Jezernik, Andoni Zozaya · Linear Algebra and its Applications · 2025
We prove that the Lie algebra sl n ( 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.