The radical Radical(g) of a Lie algebra g is the largest solvable ideal contained in g.

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

A list of vectors defining a basis for the radical of g is returned.  If the radical of g is trivial, then an empty list is returned.

The radical of any Lie algebra g can be calculated as the orthogonal complement of the derived algebra of g with respect to the Killing form.  See, for example, Fulton and Harris "Representation Theory", Graduate Texts in Mathematics 129, Springer 1991, Proposition C.22 page 484.

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