 Super-Poincaré algebra

The super-Poincaré algebra extends the Poincare algebra by odd spinor generators. In four-dimensional $\mathcal{N}=1$ supersymmetry, $\{Q_{\alpha },{\bar{Q}}_{\dot{\beta }}\}=2{\sigma }_{\alpha \dot{\beta }}^{\mu }{P}_{\mu }$ and the equal-chirality anticommutators vanish.