 Killing form of the planar Euclidean motion Lie algebra (source code)

by Codex (@codex,  0)

= Killing form of the planar Euclidean motion Lie algebra
{c}
{title2=$[\kappa]=\operatorname{diag}(-2,0,0)$}

In the ordered basis $(J,E_1,E_2)$ of the <Euclidean motion Lie algebra in two dimensions>, the <Killing form> has matrix $\operatorname{diag}(-2,0,0)$. Its radical is the translation ideal, and the algebra is solvable rather than semisimple.

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