 Poincare algebra

The Poincare algebra is generated by translations $P^{\mu }$ and Lorentz transformations $M^{\mu \nu }$. Its mixed commutator is $[M^{\mu \nu },P^{\rho }]=i({\eta }^{\nu \rho }{P}^{\mu }-{\eta }^{\mu \rho }{P}^{\nu })$.