References & Citations
Mathematics > Rings and Algebras
Title: Two-generation of traceless matrices over finite fields
(Submitted on 17 Apr 2024 (v1), last revised 15 May 2024 (this version, v2))
Abstract: We prove that the Lie algebra $\mathfrak{sl}_n(\textbf{F}_q)$ 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.
Submission history
From: Andoni Zozaya [view email][v1] Wed, 17 Apr 2024 10:44:39 GMT (15kb)
[v2] Wed, 15 May 2024 21:30:49 GMT (16kb)
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