High Quality Content by WIKIPEDIA articles! In physics and mathematics, the Poincare group, named after Henri Poincare, is the group of isometries of Minkowski spacetime. 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. Another way of putting it is the Poincare group is a group extension of the Lorentz group by a vector representation of it. Its positive energy unitary irreducible representations are indexed by mass (nonnegative number) and spin (integer or half integer), and are associated with particles in quantum mechanics.

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