 Orientation-preserving affine group of the real line (source code)

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= Orientation-preserving affine group of the real line
{title2=$\operatorname{Aff}^+(\mathbb R)$}

= Real affine group
{synonym}

The <real affine group> used here is the orientation-preserving subgroup of the <affine group> on the real line. It acts by $x\mapsto e^ax+b$ and has multiplication $(a,b)(a',b')=(a+a',b+e^ab')$. The positive dilation distinguishes this connected component from the full group, which also contains negative dilations.

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