Relation between the range of an elementary 3-particle 2-body operator and the convex structure of the set of fermion 3-representable 2-density operators

It is shown that the reduced 2-particle density operator corresponding to any function from the range of an elementary 3-particle 2-body operator 3Pg2 Λ l1 is an extreme point of the convex set of fermion 3-representable 2-density operators. The operator 3Pg2 Λ l1 ≡ A3 Σl≤i<j≤3Pg2(i, j)A3 n a 3-particle antisymmetric finite-dimensional Hilbert space. Pg2 denotes the projection operator onto a 2-particle antisymmetric function g2, I1 is the 1-particle identity operator, while A3 denotes the 3-particle antisymmetrizing operator.