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Some Collineations Preserving Cross-Ratio in some Moufang-Klingenberg Planes

Authors: Suleyman Ciftci, Atilla Akpinar, Basri Celik


In this paper we are interested in Moufang-Klingenberg planesM(A) defined over a local alternative ring A of dual numbers. We show that some collineations of M(A) preserve cross-ratio.

Keywords: Moufang-Klingenberg planes, local alternative ring, projective collineation, cross-ratio.

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[1] A. Akpinar, B. Celik and S. Ciftci, Cross-ratios and 6-figures in some Moufang-Klingenberg planes. Bulletin of the Belgian Math. Soc.-Simon Stevin 15(2008), 49-64.
[2] C.A. Baker, N.D. Lane and J.W. Lorimer. A coordinatization for Moufang-Klingenberg planes. Simon Stevin 65(1991), 3-22.
[3] J.L. Bell. The art of the intelligible: An elementary survey of mathematics in its conceptual development. Kluwer Acad. Publishers, The Netherland, 2001.
[4] A. Blunck. Cross-ratios in Moufang planes. J. Geometry 40(1991), 20- 25.
[5] A. Blunck. Projectivities in Moufang-Klingenberg planes. Geom. Dedicata 40(1991), 341-359.
[6] A. Blunck. Cross-ratios over local alternative rings. Res. Math. 19 (1991), 246-256.
[7] A. Blunck. Cross-ratios in Moufang-Klingenberg planes. Geom. Dedicata 43(1992), 93-107.
[8] B. Celik, A. Akpinar and S. Ciftci. 4-Transitivity and 6-figures in some Moufang-Klingenberg planes. Monatshefte f¨ur Mathematik 152(2007), 283-294.
[9] S. Ciftci and B. Celik. On the cross-ratios of points and lines in Moufang planes. J. Geometry 71(2001), 34-41.
[10] J.C. Ferrar. Cross-ratios in projective and affine planes. in Plaumann, P. and Strambach, K., Geometry - von Staudt-s Point of View (Proceedings Bad Windsheim, 1980), Reidel, Dordrecht, (1981) 101-125.
[11] D.R. Hughes and F.C. Piper. Projective planes. Springer, New York, 1973.
[12] G. Pickert. Projektive Ebenen. Springer, Berlin, 1955.
[13] R.D. Schafer. An introduction to nonassociative algebras. Dover Publications, New York, 1995.
[14] F.W. Stevenson. Projective planes. W.H. Freeman Co., San Francisco, 1972.