gives the Levi's decomposition of the Lie Algebra L.
  • The Lie algebra L can be provided either from their structure constants or their infinitesimal generator representation. Depending on that, the resulting subalgebra will be expresses either using the symbolic notation with X[i] denoting ith base element of the Lie algebra or by their infinitesimal generator representation.
  • Levi's theorem states that every Lie algebra can be decomposed to a semi-direct sum of its solvable radical and a semi-simple subalgebra called Levi subalgebra.
  • If the provided Lie algebra is semi-simple or solvable LeviDecomposition will give the Lie algebra itself.