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On a model for non commutative geometric spaces

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Abstract

A model for non commutative geometries is proposed which describes axioms by corresponding equations. Applications are made.

This is a basic article on a model for description of non commutative geometries. Basic tools are developed for further use. We give some examples and applications and solve some open problems of this theory. All results apply to classical geometry, too, since non commutative geometry is a natural generalization of classical affine geometry, introduced by J.André (cf.[A]).

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References

  1. ANDRÉ,J.: On finite noncommutative affine spaces. In: combinatorics, 2nd ed. (M.Hall jr. and J.H.van Lint, eds.) Proceedings of an Advanced Inst. on Combinat. (Breukelen 1974) Amsterdam, Math. Centrum. pp 65–113

  2. ANDRÉ,J.: Some new results on incidence structures. Atti dei convegni lincei 17. Accademia nazionale dei lincei, Roma 1976. pp 201–222

  3. ANDRÉ,J.: Nicht kommutative Geometrie und verallgemeinerte Hughes-Ebenen. Math. Zeitschrift177 (1981), 449–462

    Google Scholar 

  4. ANDRÉ, J.: Eine geometrische Kennzeichnung imprimitiver Frobeniusgruppen. Abhandlungen Math. Seminar Univ. Hamburg Band51 (1981), 120–135

    Google Scholar 

  5. ANDRÉ,J.: Coherent configurations and noncommutative spaces. Geometriae Dedicata13 (1983), 351–360

    Google Scholar 

  6. HAUPTMANN, W.: Kohärente Konfigurationen, quasiaffine Räume und distanz-reguläre Graphen. Mitteilungen Math. Seminar Giessen144 (1980), 1–83

    Google Scholar 

  7. LANG,S.: Algebra, 3rd printing. Addison-Wesley Publ. Comp.

  8. PFALZGRAF,J.: Über eine Möglichkeit zur Beschreibung geometrischer Räume. Ausfaktorisieren von Relationen. Math. Inst. Univ. des Saarlandes, Saarbrücken 1982

    Google Scholar 

  9. PFALZGRAF,J.: Über ein Modell für nicht kommutative geometrische Räume. Dissertation. Math. Inst. Univ. des Saarlandes, Saarbrücken 1984.

    Google Scholar 

  10. TAMASCHKE,O.: Projektive Geometrie II. Bibliographisches Institut Mannheim 1972, Band 838

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Pfalzgraf, J. On a model for non commutative geometric spaces. J Geom 25, 147–163 (1985). https://doi.org/10.1007/BF01220477

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  • DOI: https://doi.org/10.1007/BF01220477

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