Sym Paclet Symbol

SemiDirectSumQ

SemiDirectSumQ[L, V, W]
gives True if the Lie algebra L can be expressed as a semidirect sum of the two subalgebras V, W and False otherwise.

To use SemiDirectSumQ, you first need to load the SYM Package using Needs["SYM`"].

The Lie algebra L and its subalgebras can be provided either from their structure constants or their infinitesimal generator representation. When providing the Lie algebra L with its structure constants denote the elements of the subspaces by using the symbol X, e.g. {X[1], X[4]}.