Sym Paclet Symbol

# OrthogonalComplement

 OrthogonalComplement[L, V] gives the orthogonal complement of subspace V in L with respect to the Killing form. OrthogonalComplement[L, V, ip]gives the orthogonal complement of subspace V in L with respect to a user defined inner product ip.
• The Lie algebra L 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]}.
• If VL is a subspace of L, then the set {xLkL(x, y)=0 yV} is called the orthogonal complement of V in L with respect to kL.
• Depending of the input, OrthogonalComplement 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.
Orthogonal complement using the infinitesimal representation of the Lie algebra
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Orthogonal complement using the structure constants of the Lie algebra.
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