Two New Collineations of some Moufang-Klingenberg Planes

Authors: Atilla Akpinar, Basri Çelik

Abstract:

In this paper we are interested in Moufang-Klingenberg planesM(A) defined over a local alternative ring A of dual numbers. We introduce two new collineations of M(A).

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

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1074747

References:

[1] Baker C.A., Lane N.D., Lorimer J.W. A coordinatization for Moufang- Klingenberg planes. Simon Stevin 65(1991), 3-22.
[2] Blunck A. Cross-ratios over local alternative rings. Res. Math. 19(1991), 246-256.
[3] Blunck A. Cross-ratios in Moufang-Klingenberg planes. Geom. Dedicata 43(1992), 93-107.
[4] Celik B., Akpinar A., Ciftci S. 4-Transitivity and 6-figures in some Moufang-Klingenberg planes. Monatshefte f¨ur Mathematik 152(2007), 283-294.
[5] Hughes D.R, Piper F.C. Projective planes. Springer: New York (1973).
[6] Pickert G. Projektive Ebenen. Springer: Berlin (1955).
[7] Schafer R.D. An introduction to nonassociative algebras. Dover Publications, New York, (1995).
[8] Stevenson F.W. Projective planes. W.H. Freeman Co.: San Francisco (1972).