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.
OrthogonalComplement[L, V, ip] applies the function ip to pairs of elements to determine their orthogonality. The default function ip is KillingForm.
L is a subspace of L, then the set {x
L
kL(x, y)=0 
y
EXAMPLES
Basic Examples 
