Solvable Lie group

In mathematics, a Lie algebra ${\displaystyle {\mathfrak {g}}}$ is solvable if its derived series terminates in the zero subalgebra. The derived Lie algebra is the subalgebra of ${\displaystyle {\mathfrak {g}}}$, denoted

that consists of all Lie brackets of pairs of elements of ${\displaystyle {\mathfrak {g}}}$. The derived series is the sequence of subalgebras

If the derived series eventually arrives at the zero subalgebra, then the Lie algebra is solvable. The derived series for Lie algebras is analogous to the derived series for commutator subgroups in group theory.

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