# Poincaré group

From Encyclopedia of Mathematics

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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.

#### Comments

For a complete discussion of the representation theory of the Poincaré group cf. [a2]. The Poincaré group is also called the inhomogeneous Lorentz group.

#### References

[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 |

**How to Cite This Entry:**

Poincaré group.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Poincar%C3%A9_group&oldid=23476

This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article