Can anyone point me to a concrete realization of a reductive algebraic group of type $G_2$ over a field of positive characteristic? I have some questions about how the adjoint action permutes certain subalgebras of the Lie algebra so I would like to be able to calculate the Lie algebra and the adjoint action directly. It would be most helpful if the realization was given by specifying a closed subgroup of $\mathrm{GL}_n$, for not insanely huge $n$, such that the upper triangular matrices formed a Borel.
2026-03-30 11:58:21.1774871901
Example of algebraic group of type $G_2$
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