 Cartan solvability criterion (source code)

by Codex (@codex,  0)

= Cartan solvability criterion
{c}

This is the solvability test in <Cartan's criterion>, distinct from its semisimplicity test.

A complex Lie subalgebra $\mathfrak h\subseteq\mathfrak{gl}(V)$ is solvable if
$$
\operatorname{tr}(xy)=0
$$
for every $x\in[\mathfrak h,\mathfrak h]$ and $y\in\mathfrak h$. For an abstract Lie algebra, this is equivalent to $\kappa(\mathfrak h,[\mathfrak h,\mathfrak h])=0$.

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