If we assume field $F$ has characteristic $p$, can we get the statement that $sl(n;F)$ is a simple Lie algebra? Here integer $n$ is not a multiple of $p$.
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Compare https://math.stackexchange.com/q/1598356/96384, https://math.stackexchange.com/q/467539/96384, https://math.stackexchange.com/q/1409744/96384 and possibly more. – Torsten Schoeneberg Nov 12 '20 at 17:24
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Yes, I have read them, but my question is more general. Is there some references to get an answer for the more general question? – Inuyasha Nov 12 '20 at 17:44
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1The proof here does work for all $n\ge 3$, too. A reference is the book by George Seligman on modular Lie algebras. – Dietrich Burde Nov 12 '20 at 19:18