The group of motions of Minkowski space. The Poincaré group is the semi-direct product of the group of Lorentz transformations (cf. Lorentz transformation) and the group of four-dimensional displacements (translations). The Poincaré group is called after H. Poincaré, who first (1905) established that the Lorentz transformations form a group.
For a complete discussion of the representation theory of the Poincaré group cf. [a2]. The Poincaré group is also called the inhomogeneous Lorentz group.
|[a1]||W. Rühl, "The Lorentz group and harmonic analysis" , Benjamin (1970)|
|[a2]||A.O. Barut, R. Raçzka, "Theory of group representations and applications" , 1–2 , PWN (1977) pp. Chapt. 17|
Poincaré group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Poincar%C3%A9_group&oldid=23476