ProductSpace[L, V, W]
gives the product space [V, W] between two subalgebras V, W of a Lie algebra L.
gives the product space [L, L] of a Lie algebra L.
  • 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.