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]}.
The command checks if the supplied subspaces V, W are indeed Lie subalgebras of Lie algebra L.
Depending of the input, ProductSpace will return the base which spans the product space either by using the representation provided or the syntax for the subspaces using the symbol X.