nLab Galilean group

Idea

The Euclidean group $Iso(D)$ is the isometry group of Euclidean space $\mathbb{R}^D$, generated from rigid translations rotations and reflections.

For $D=3$ this is part of the canonical symmetry group of ordinary nonrelativistic classical mechanics/classical field theory, thus known as the Galilean group, which in addition contains time-translations and “Galilean boosts”:

This is a 10 dimensional Lie group which may be understood as the Inönü-Wigner contraction of the Poincaré group given by the limit in whuch the speed of light goes to infinity.

Related concepts

• classical mechanics

• translation group

• Lorentz group, Poincare group

• super Euclidean group

• space group

  • wallpaper group

References

Textbook account:

• Mark A. Armstrong, chapter 24 of: Groups and Symmetry, Undergraduate Texts in Mathematics, Springer (1988) [doi:10.1007/978-1-4757-4034-9, pdf]

See also:

• Wikipedia, Galilean group

• Wikipedia, Euclidean group

• David R. Hilbert, Nick Huggett, Groups in Mind, Philosophy of Science 73 (5):765-777 (2006) (doi:10.1086/518635, pdf)