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Chain spaces over Jordan systems

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Abstract

Strong Jordan systems are certain subspaces of associative algebras closed under inversion and with many units. Every strong Jordan system gives rise to a chain space. We show that every homotopism of Jordan systems yields a morphism between the associated chain spaces and vice versa. By this, we obtain an isomorphy of categories.

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References

  1. C.G. Bartolone, Jordan homomorphisms, chain geometries and the fundamental theorem. Abh. Math. Sem. Hamburg59 (1989), 93–99.

    MATH  MathSciNet  Google Scholar 

  2. W. Benz, Vorlesungen über Geometrie der Algebren. Springer, Berlin, 1973.

    MATH  Google Scholar 

  3. A. Blunck, Chain geometries over local alternative algebras, J. Geom.44 (1992), 33–14.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Herzer, On isomorphisms of chain geometries, Note di Mat.8 (1987), 251–270.

    MathSciNet  Google Scholar 

  5. A. Herzer, Die Kategorie der Kettengeometrien, Res. Math.12 (1987), 278–288.

    MATH  MathSciNet  Google Scholar 

  6. A. Herzer, On sets of subspaces closed under reguli, Geom. Dedicata41 (1992), 89–99.

    MATH  MathSciNet  Google Scholar 

  7. A. Herzer, Chain Geometries, in: Handbook of Incidence Geometry, ed. F. Buekenhout, North-Holland, Amsterdam, to appear.

  8. A. Herzer, Private communication.

  9. N. Jacobson, Structure and Representations of Jordan Algebras, AMS Coll. Publ.39, Providence, 1968.

  10. H.-J. Kroll, Unterräume von Kettengeometrien und Kettengeometrien mit Quadrikenmodell, Res. Math.19 (1991), 327–334.

    MATH  MathSciNet  Google Scholar 

  11. H. Mäurer, R. Metz andW. Nolte, Die Automorphismengruppe der Möbiusgeometrie einer Körpererweiterung, Aequationes Math.21 (1980), 110–112.

    Article  MATH  MathSciNet  Google Scholar 

  12. G. Pickert, Projektive Ebenen, Springer, Berlin, 1955.

    MATH  Google Scholar 

  13. K. Sörensen, Der Fundamentalsatz für Projektionen, Mitt. Math. Ges. Hamburg11 (1985), 303–309.

    MATH  MathSciNet  Google Scholar 

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  1. Fachbereich Mathematik der TH Darmstadt, Schloßgartenstraße 7, 64289, Darmstadt, Germany

    A. Blunck

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  1. A. Blunck
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Blunck, A. Chain spaces over Jordan systems. Abh.Math.Semin.Univ.Hambg. 64, 33–49 (1994). https://doi.org/10.1007/BF02940773

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  • DOI: https://doi.org/10.1007/BF02940773

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