A pair of subalgebras [R, S] in a Lie algebra define a Levi decomposition if R is the radical of g, S is a semisimple subalgebra, and g = R + S (vector space direct sum).  Since the radical is an ideal we have [R, R] in R, [R, S] in R, and [S, S] in S.  The radical R is unique, the semisimple subalgebra S in a Levi decomposition is not.

Query([R, S], "LeviDecomposition") returns true if the pair R, S is a Levi decomposition of g and false otherwise.

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