The lower central series of a Lie algebra g is the sequence of subalgebras recursively defined by g_(k + 1) = [g, 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 lower central series ends in the zero subspace, the Lie algebra is called nilpotent.
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