The Chirality operators for Heisenberg Spin Systems
  The ground state of closed Heisenberg spin chains with an odd number of sites has a chiral degeneracy, in addition to a two-fold Kramers degeneracy. A non-zero chirality implies that the spins are not coplanar, and is a measure of handedness. The chirality operator, which can be treated as a spin-1/2 operator, is explicitly constructed in terms of the spin operators, and is given as commutator of Permutation operators. 
V. Subrahmanyam (International Center for Theoretical Physics, POBox   586, Trieste, Italy)