Poincaré groupIn physics, the Poincaré group is the group of isometries of Minkowski space. It is a 10-dimensional noncompact Lie group. The Abelian group of translations is a normal subgroup while the Lorentz group is a subgroup, the stabilizer of a point.
In accordance with the Erlanger program, the geometry of Minkowski space is defined by the Poincaré group.
In component form, the Lie algebra of the Poincaré group satisfies