nLab affine group

For affine groups in the antithesis interpretation of constructive mathematics, see A-group.

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Definition

Given an affine space underlying a vector space $V$, then its affine group is its group of automorphisms, i.e. the semidirect product group

$$Aff(V) = V \rtimes GL(V)$$

of the translation group of $V$ and the general linear group of $V$.

Related concepts

• affine symplectic group

• Galilei group

• Poincare group