 Solution

The Coleman–Mandula theorem says that, under its assumptions on a nontrivial analytic relativistic S-matrix and the particle spectrum, every continuous bosonic symmetry algebra is a direct sum of the Poincare algebra and an internal symmetry algebra. Supersymmetry becomes possible by weakening the assumption that the symmetry algebra is an ordinary Lie algebra: a Z2-graded Lie superalgebra admits odd generators whose bracket is an anticommutator. The Haag–Łopuszański–Sohnius theorem then classifies the allowed extension and leads to the Super-Poincaré algebra.