= Special conformal transformation
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A special conformal transformation is a <conformal transformation> whose finite Euclidean form in one sign convention is $x'^i=(x^i-b^i x^2)/(1-2b\cdot x+b^2x^2)$ wherever the denominator is nonzero. Its position-dependent scale change preserves local angles.
In three boundary dimensions, the three parameters $b^i$ supplement translations, rotations and <dilation> to form the ten-dimensional <de Sitter isometry> algebra. The full transformation of the flat-slicing <spacetime> also acts on <conformal time>; the boundary formula alone is not that bulk transformation. A matter equation with a propagation speed different from the metric <speed of light> generally need not preserve these isometries.
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