Poincaré group

The group $Poin(3,1)$ or $ISO(3,1)$ is the semidirect product of translations ${\mathbb{R}}^4$ with the Lorentz group $O(3,1)$:

Poincaré symmetry is the full symmetry of special relativity. It includes:

• translations (displacements) in time and space, forming the Abelian Lie group of translations on space-time;
• rotations in space, forming the non-Abelian Lie group of three-dimensional rotations;
• boosts, or Lorentz transformations connecting two uniformly moving observers.

It substituted the Galilean group $Gal(3)$. See \section{Development of SR} at notasfisica.tex, and write it to obsidian.