= 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>.
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