Translation Group
Intuitive
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
Concrete
The group of translations is always equivalent to the space we are considering. So if we are dealing with objects in $\mathbb{R}^3$ the translation group is $\mathbb{R}^3$. If we consider objects in Minkowski space $\mathbb{R}^{3,1}$, the group of translations is $\mathbb{R}^{3,1}$.
Abstract
The motto in this section is: the higher the level of abstraction, the better.