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Aug 16, 2015 at 1:49 vote accept Jianrong Li
Aug 15, 2015 at 19:55 comment added YCor Take the invertible derivation mapping $e_i$ to $ie_i$, thus defining a 6-dimensional semidirect product of your Lie algebra with a 1-dimensional Lie algebra. The resulting Lie algebra has zero center and hence its adjoint representation is faithful (and easily computable).
Aug 15, 2015 at 13:29 answer added Dietrich Burde timeline score: 6
Aug 15, 2015 at 12:45 history asked Jianrong Li CC BY-SA 3.0