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Reflection loops of spaces with congruence and hyperbolic incidence structure

Alexander Kreuzer — 2004

Commentationes Mathematicae Universitatis Carolinae

In an absolute space ( P , 𝔏 , , α ) with congruence there are line reflections and point reflections. With the help of point reflections one can define in a natural way an addition + of points which is only associative if the product of three point reflection is a point reflection again. In general, for example for the case that ( P , 𝔏 , α ) is a linear space with hyperbolic incidence structure, the addition is not associative. ( P , + ) is a K-loop or a Bruck loop.

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