The derived algebra of a Lie algebra g is the span of the set of vectors [x, y] for all x, y in g.  It is an ideal in g.

DerivedAlgebra(LieAlgName) calculates the derived algebra of the Lie algebra g defined by LieAlgName.  If no argument is given, then the derived algebra  of the current Lie algebra is found.

DerivedAlgebra(S) calculates the derived algebra of the Lie subalgebra S (viewed as a Lie algebra in its own right).

A list of vectors defining a basis for the derived algebra of g (or S) is returned.  If the derived algebra of g is trivial, then an empty list is returned.

The command DerivedAlgebra is part of the DifferentialGeometry:-LieAlgebras package.  It can be used in the form DerivedAlgebra(...) only after executing the commands with(DifferentialGeometry) and with(LieAlgebras), but can always be used by executing DifferentialGeometry:-LieAlgebras:-DerivedAlgebra(...).