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Abstract

Automorphisms of non-trivial spine spaces are either, type-preserving, or type-exchanging, that is, they map stars onto stars or exchange them with tops. In the first case they are given by semi-linear bijections, in the latter, by sesqui-linear forms.

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References

  1. E. Artin,Geometric Algebra. Interscience, 1957.

  2. W. Benz,Geometrishe Transformationen. B. I. Wiessenschaftsverlag, 1992.

  3. A. BicharaandG. Tallini, On a characterization of Grassmann space representing theh -dimensional subspaces in a projective space.Annals of Discrete Math. 181983, 113-132.

  4. A. Blunck andH. Havlicek, Affine spaces within projective spaces.Results Math. 36, 3–4 (1999), 237–251.

    MATH  MathSciNet  Google Scholar 

  5. H. Brauner, Über die von Kollineationen projektiver Räume induzierten Geradenabbildungen.Sitz. Ber. österr. Akad. Wiss., math.-naturw. Kl. Abt. II 197 (1998), 327–332.

    MathSciNet  Google Scholar 

  6. J. Dieudonné,La géométrie des groupes classiques. Springer-Verlag, 1971.

  7. H. Havlicek, Isomorphisms of affine Plücker spaces. In Proc. of the 4th International Conference of Geometry Thessaloniki 1996,N. K. Artémiads andN. K. Stephanidis (eds.), Aristoteles University of Thessaloniki, 1997, pp. 171–178.

  8. ——, Chow’s theorem for linear spaces.Discrete Mathematics 208/209 (1999), 319–324.

    Article  MathSciNet  Google Scholar 

  9. W. V. D. Hodge andD. Pedoe,Methods of algebraic geometry, vol. II. Cambridge University Press, 1968.

  10. W.-L. Huang, Adjacency preserving transformations of Grassmann spaces.Abh. Math. Sem. Univ. Hamb. 68 (1998), 65–77.

    Article  MATH  Google Scholar 

  11. H. Karzel andH. Meissner, Geschütze Inzidenzgruppen und normale Fastmoduln.Abh. Math. Sem. Univ. Hamb. 31 (1967), 69–88.

    Article  MATH  MathSciNet  Google Scholar 

  12. H. Karzel andI. Pieper, Bericht über geschlitzte inzidenzgruppen.Jber. Deutsch. Math-Verein. 70 (1970), 70–114.

    Google Scholar 

  13. I. R. Porteous,Topological geometry. Cambridge University Press, 1981.

  14. K. Prażmowski On a construction of affine grassmannians and spine spaces.J. Geom. 72 (2001), 172–187.

    Article  MATH  MathSciNet  Google Scholar 

  15. K. Prażmowski andM. Żynel, Geometry of the structure of linear complements. To appear inJ. Geom.

  16. G. Tallini, Partial line spaces and algebraic varieties.Symp. Math. 28 (1986), 203–217.

    MathSciNet  Google Scholar 

  17. M. Żynel, Subspaces and embeddings of spaces of pencils. Submitted toRend. Sem. Mat. Messina.

  18. M. Żynel, Finite grassmannian geometries.Demonstratio Math. XXXIV 1 (2001), 145–160.

    Google Scholar 

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Correspondence to K. Prażmowski or M. Zynel.

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Prażmowski, K., Zynel, M. Automorphisms of spine spaces. Abh.Math.Semin.Univ.Hambg. 72, 59–77 (2002). https://doi.org/10.1007/BF02941665

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