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Point-Reflection Geometries, Geometric K-Loops and Unitary Geometries

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Abstract

There are reflection geometries to which correspond K- loops (P,+,F) with an incidence fibration F (= incidence partition), where F consists of proper subloops which are not groups. Such examples are derived from certain unitary geometries.

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References

  1. F.B Achmann: Zur Begründung der Geometrie aus dem Spiegelungsbegriff. Math. Ann. 123, 341–344, (1951).

    Article  MathSciNet  MATH  Google Scholar 

  2. H. Karzel: Recent developments on absolute geometries and algebraization by K-loops. Submitted to Discrete Mathematics. (1996).

  3. H. Karzel, A. Konrad: Reflection groups and K-loops. J.Geom. 52, 120–129, (1995).

    Article  MathSciNet  MATH  Google Scholar 

  4. C.F. Manara, M. MarchI: On a class of reflection geometries. 1st. Lomb. Rend. Sc. A 125,2, 203–217, (1991)

    MathSciNet  MATH  Google Scholar 

  5. H.A. Schmidt: Die Dualität von Inzidenz und Senkrechtstehen in der absoluten Geometrie. Math. Ann. 118, 609–625, (1941/1943).

    Article  MATH  Google Scholar 

  6. G. Thomsen: Grundlagen der Elementargeometrie in gruppenalgebraischer Behandlung. Hamburger Math. Einzelschr. 15, (1933)

  7. H. Wiener: Über Grundlagen und Außau der Geometrie. Jber DMV 1, 45-48, (1890/91).

    Google Scholar 

  8. H. Wiener: Sechs Abhandlungen über das Rechnen mit Spiegelungen. Abdrucke aus den Ber. der math.-phys. Kl. der Kgl. Sachs. Ges. der Wiss. 1890, 1891, 1893, Leipzig 1893.

  9. E.Zizioli: Fibered incidence loops and kinematic loops. J.Geom. 30, 144–156, (1987).

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Elisabetta Gabrieli.

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Gabrieli, E., Karzel, H. Point-Reflection Geometries, Geometric K-Loops and Unitary Geometries. Results. Math. 32, 66–72 (1997). https://doi.org/10.1007/BF03322525

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  • DOI: https://doi.org/10.1007/BF03322525

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