Supersymmetry algebra

In theoretical physics, a supersymmetry algebra (or SUSY algebra) is a mathematical formalism for describing the relation between bosons and fermions. The supersymmetry algebra contains not only the Poincaré algebra and a compact subalgebra of internal symmetries, but also contains some fermionic supercharges, transforming as a sum of N real spinor representations of the Poincaré group. Such symmetries are allowed by the Haag–Lopuszanski–Sohnius theorem. When N>1 the algebra is said to have extended supersymmetry. The supersymmetry algebra is a semidirect product of a central extension of the super-Poincaré algebra by a compact Lie algebra B of internal symmetries.