Do the Suzuki and Ree groups of Lie type have associated Lie algebras over finite fields in the same way that the other groups of Lie type do? These algebras would be 5-dimensional over $\mathbb{F}_{2^{2m-1}}$ ($^2 \mathfrak{b}_2$), 7-dimensional over $\mathbb{F}_{3^{2m-1}}$ ($^2 \mathfrak{g}_2$), and 26-dimensional over $\mathbb{F}_{2^{2m-1}}$ ($^2 \mathfrak{f}_4$).
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$\begingroup$ An ignorant question: couldn't you just take the twisted-Frobenius fixed points in the Lie algebra over $\overline{\mathbb F_p}$? $\endgroup$– LSpiceCommented Nov 25, 2022 at 4:18
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