Two-site support of the Pauli-matrix Affleck--Kennedy--Lieb--Tasaki tensor

Because ${\sigma }_i{\sigma }_j={\delta }_{ij}I+i{\epsilon }_{ijk}{\sigma }_k$, the two-site image of the Pauli-matrix AKLT tensor is the direct sum of the scalar and antisymmetric subspaces, which have total spin zero and one. Its orthogonal complement is the symmetric traceless total-spin-two subspace.