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Point-line characterizations of buildings

Part of the Lecture Notes in Mathematics book series (LNMCIME,volume 1181)

Keywords

  • Projective Space
  • Polar Space
  • Chevalley Group
  • Generalize Quadrangle
  • Spherical Type

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9. References

  1. Aschbacher, M., A characterization of Chevalley groups over fields of odd characteristic, Annals of Math. 106 (1977) 353–468.

    CrossRef  MATH  MathSciNet  Google Scholar 

  2. Biggs, N.L. Algebraic Graph Theory, Cambridge University Press, Cambridge, 1974.

    CrossRef  MATH  Google Scholar 

  3. Blokhuis A. & A.E. Brouwer, private communication.

    Google Scholar 

  4. Bourbaki, N., Groupes et algèbres de Lie, Chap. IV, V, VI, Hermann, Paris, 1968.

    Google Scholar 

  5. Brouwer, A.E. & A.M. Cohen, Some remarks on Tits geometries, Indagationes Mathematicae 45 (1983)

    Google Scholar 

  6. Brouwer, A.E. & A.M. Cohen, Local recognition of some Tits geometries of classical type, to appear in Geom. Dedicata.

    Google Scholar 

  7. A.E. Brouwer & H.A. Wilbrink, The structure of near polygons with quads, Geom. Dedicata 14(1983) 145–176. Amsterdam, 1981.

    CrossRef  MATH  MathSciNet  Google Scholar 

  8. Buekenhout, F., Une caractérisation des espaces affines basée sur la notion de droite, Math. Zeitschr. 111 (1969) 367–371.

    CrossRef  MATH  MathSciNet  Google Scholar 

  9. Buekenhout, F., An approach to building geometries based on points, lines and convexity, European J. Combinatorics 3 (1982) 103–118.

    MATH  MathSciNet  Google Scholar 

  10. Buekenhout, F., A characterization of polar spaces, Simon Stevin 53 (1973) 3–7.

    MathSciNet  Google Scholar 

  11. Buekenhout, F., Cooperstein's Theory, Simon Stevin 57 (1983) 125–140.

    MATH  MathSciNet  Google Scholar 

  12. Buekenhout, F. & B. Fischer, A locally dual polar space for the Monster, preprint.

    Google Scholar 

  13. Buekenhout, F. & X. Hubaut, Locally polar spaces and related rank 3 groups, J. Algebra 45 (1977) 393–434.

    CrossRef  MathSciNet  Google Scholar 

  14. Buekenhout, F. & C. Lefèvre, Generalized Quadrangles in projective spaces, Arch. Math. 25 (1974) 540–552.

    CrossRef  MATH  Google Scholar 

  15. Buekenhout, F. & E.E. Shult, On the foundation of polar geometry, Geom. Dedicata 12 (1982) 75–85.

    MathSciNet  Google Scholar 

  16. Buekenhout, F. & A. Sprague, Polar spaces having some line of cardinality two, J. Combinatorial Theory (A) 33 (1982) 223–238.

    CrossRef  MATH  MathSciNet  Google Scholar 

  17. Buset, D., Graphs which are locally a cube, Discrete Math. 46 (1983) 221–226.

    CrossRef  MATH  MathSciNet  Google Scholar 

  18. Cameron, P.J., Dual polar spaces, Geom. Dedicata 12 (1982) 75–85.

    CrossRef  MATH  MathSciNet  Google Scholar 

  19. Cameron, P.J. & W.M. Kantor, 2-Transitive and antiflag transitive collineation groups of finite projective spaces, J. Algebra 60 (1979) 384–422.

    CrossRef  MATH  MathSciNet  Google Scholar 

  20. Cohen, A.M., An axiom system for metasymplectic spaces, Geom. Dedicata 12 (1982) 417–433.

    CrossRef  MATH  MathSciNet  Google Scholar 

  21. Cohen, A.M., On the points and lines of metasymplectic spaces, Annals of Discrete Math. 18 (1983) 193–196.

    MATH  Google Scholar 

  22. Cohen, A.M., On a theorem of Cooperstein, European J. Combinatorics 4 (1983) 107–126.

    MATH  Google Scholar 

  23. Cohen, A.M. & B.N. Cooperstein, A characterization of some geometries of exceptional Lie type, Geom. Dedicata 15 (1983) 73–105.

    CrossRef  MATH  MathSciNet  Google Scholar 

  24. Cohen, A.M. & B.N. Cooperstein, On the local recognition of finite metasymplectic spaces, preprint.

    Google Scholar 

  25. Cooperstein, B.N., Some geometries associated with parabolic representations of groups of Lie type, Canadian J. Math. 28 (1976) 1021–1031.

    CrossRef  MATH  MathSciNet  Google Scholar 

  26. Cooperstein, B.N., A characterization of some Lie incidence structures, Geom. Dedicata 6 (1977) 205–258.

    CrossRef  MATH  MathSciNet  Google Scholar 

  27. Dienst, K.J., Verallgemeinerte Vierecke in projektiven Räumen, Arch. Math. 35 (1980) 177–186.

    CrossRef  MATH  MathSciNet  Google Scholar 

  28. Hall, J.I. & E.E. Shult, Locally cotriangular graphs, to appear.

    Google Scholar 

  29. Hanssens, G.J.J.J., Punt-rechte meetkunden van sferische gebouwen, Thesis, R.U. Gent, 1984.

    Google Scholar 

  30. Johnson, P. & E.E. Shult, Local characterizations of polar spaces, to appear in Geom. Dedicata.

    Google Scholar 

  31. Lefevre-Percsy, C., Polar spaces embedded in projective space, pp.216–220 in: Finite Geometries and Designs, (P.J. Cameron, J.W.P. Hirschfeld, D.R. Hughes, eds.) LMS Lecture Note Series 49, Cambridge University Press, Cambridge, 1981.

    Google Scholar 

  32. Ronan, M.A., Extending locally truncated buildings and chamber systems, to appear.

    Google Scholar 

  33. Ronan, M.A., Coverings of certain finite geometries, pp.316–331 in: Finite Geometries and Designs, (P.J. Cameron, J.W.P. Hirschfeld, D.R. Hughes, eds.) LMS Lecture Note Series 49, Cambridge University Press, Cambridge, 1981.

    Google Scholar 

  34. Ronan, M.A. & S.D. Smith, Sheaf homology on buildings and modular representations of Chevalley groups, I,II,III, preprints.

    Google Scholar 

  35. Ronan, M.A. & G. Stroth, Minimal parabolic geometries for the sporadic groups, European J. Combinatorics 5 (1984) 59–91.

    MATH  MathSciNet  Google Scholar 

  36. Shult, E.E., Lie incidence geometries, pp.157–184 in:Surveys in Combinatorics, E. Keith Lloyd (ed.), London Math. Soc. Lecture Note Series 82, Cambridge University Press, Cambridge, 1983.

    Google Scholar 

  37. Shult, E.E. & A. Yanushka, Near n-gons and line systems, Geom. Dedicata 9 (1980) 1–72.

    CrossRef  MATH  MathSciNet  Google Scholar 

  38. Timmesfeld, F., Groups generated by root involutions I,II, J. Algebra 33 (1975) 75–135, 35 (1975) 367–441.

    CrossRef  MATH  MathSciNet  Google Scholar 

  39. Tits, J., Buildings of Spherical Type and Finite BN-pairs, Springer Lecture Notes in Math. 386, Springer, Berlin, 1974.

    MATH  Google Scholar 

  40. Tits, J., A local approach to buildings, pp. 519–547 in: The Geometric Vein, Ch. Davis et al. (eds.), Springer, Berlin, 1981.

    CrossRef  Google Scholar 

  41. Wells, A.L., Universal projective embeddings of the Grassmannian, half spinor, and dual orthogonal geometries, Quart. J. Math. Oxford (2) 34 (1983) 375–386.

    CrossRef  MATH  Google Scholar 

  42. Zara, F., Graphes liés aux espaces polaires, preprint.

    Google Scholar 

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© 1986 Springer-Verlag Berlin Heidelberg

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Cohen, A.M. (1986). Point-line characterizations of buildings. In: Rosati, L.A. (eds) Buildings and the Geometry of Diagrams. Lecture Notes in Mathematics, vol 1181. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075515

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  • DOI: https://doi.org/10.1007/BFb0075515

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