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Up to isomorphism, what are all the seven-dimensional simple Lie algebras over the field with three elements?

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  • $\begingroup$ Do you have a sense of the order of magnitude of the number of such algebras? (I don't.) $\endgroup$
    – LSpice
    Commented Jul 25, 2022 at 5:28
  • $\begingroup$ I’m pretty sure there are at least three. $\endgroup$
    – Daniel Sebald
    Commented Jul 25, 2022 at 5:47
  • $\begingroup$ The question is too narrow for my taste. I would be more interested in some general classification statement about simple Lie algebras over $\mathbb F_3$ (possibly of small dimension, but not just dimension $7$). $\endgroup$
    – André Henriques
    Commented Jul 25, 2022 at 5:58
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    $\begingroup$ @MatthieuRomagny it’s the simplest case that cannot be answered by using gap-system.org/Manuals/pkg/liealgdb/doc/chap0.html $\endgroup$
    – Daniel Sebald
    Commented Jul 25, 2022 at 6:38
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    $\begingroup$ @DanielSebald it would be helpful to give more context (e.g., giving the number of simple Lie algebras in dimension up to 6) $\endgroup$
    – YCor
    Commented Jul 25, 2022 at 7:46

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