Reflection loops of spaces with congruence and hyperbolic incidence structure

Alexander Kreuzer

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 2, page 303-320
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Kreuzer, Alexander. "Reflection loops of spaces with congruence and hyperbolic incidence structure." Commentationes Mathematicae Universitatis Carolinae 45.2 (2004): 303-320. <http://eudml.org/doc/249341>.

@article{Kreuzer2004,
abstract = {In an absolute space $(P, \mathfrak \{L\}, \equiv , \alpha )$ 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 $(P, \mathfrak \{L\}, \alpha )$ is a linear space with hyperbolic incidence structure, the addition is not associative. $(P,+)$ is a K-loop or a Bruck loop.},
author = {Kreuzer, Alexander},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {ordered space with congruence; point reflection; Bol loop; K-loop; ordered spaces with congruences; point reflections; Bol loops; K-loops},
language = {eng},
number = {2},
pages = {303-320},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Reflection loops of spaces with congruence and hyperbolic incidence structure},
url = {http://eudml.org/doc/249341},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Kreuzer, Alexander
TI - Reflection loops of spaces with congruence and hyperbolic incidence structure
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 2
SP - 303
EP - 320
AB - In an absolute space $(P, \mathfrak {L}, \equiv , \alpha )$ 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 $(P, \mathfrak {L}, \alpha )$ is a linear space with hyperbolic incidence structure, the addition is not associative. $(P,+)$ is a K-loop or a Bruck loop.
LA - eng
KW - ordered space with congruence; point reflection; Bol loop; K-loop; ordered spaces with congruences; point reflections; Bol loops; K-loops
UR - http://eudml.org/doc/249341
ER -

References

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