Angular momentum tensor ($L_{ab}={\sum }_s(q_{s,a}{p}_{s,b}-q_{s,b}{p}_{s,a})$)

In $D$ spatial dimensions, rotations have an antisymmetric tensor of conserved Noether charges when the dynamics is rotationally invariant. There are $D(D-1)/2$ independent rotation generators. In three dimensions the tensor is equivalent to the axial angular momentum vector through $L_i={ϵ}_{iab}{L}_{ab}/2$.