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## Main Question or Discussion Point

Does anybody know the answer of the following problem?

Show that the Lie group of Euclidean motions of R^3 has a Lie algebra g which is perfect i.e., Dg=g but g is not semisimple.

By Dg I mean the commutator [g,g] and a semisimple lie algebra is one has no nonzero solvable ideals.

Regards

Show that the Lie group of Euclidean motions of R^3 has a Lie algebra g which is perfect i.e., Dg=g but g is not semisimple.

By Dg I mean the commutator [g,g] and a semisimple lie algebra is one has no nonzero solvable ideals.

Regards