The commutator series of a Lie algebra g, sometimes called the derived series, is the sequence of subalgebras recursively defined by g^(k + 1) = [g^k, g^k], with g^0 = g. The sequence of subspaces is always decreasing with respect to inclusion or dimension, and becomes stable when g is finite dimensional. The notation [a, b] means the linear span of elements of the form [A, B], where A element a and B element b. When the commutator series ends in the zero subspace, the Lie algebra is called solvable.
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