Cross-ratios in Moufang-Klingenberg planes

Abstract

ABSVRACT. Certain geometric groups operating on a line g in a Moufang-Klingenberg plane J/ are described algebraically in terms of the underlying alternative ring R. For the case of the dual numbers R = A + Ae (A alternative field, e2= 0) a notion of cross-ratio is introduced on the line. We establish some connections between the geometric groups and the cross-ratio which are well known from classical projective planes.

n-spaces

“…O, then S 2 (R) is an octonion plane and also the MK-plane, introduced by Blunck in[4]. Moreover, for n > 2, S n (R) is the example of n-space (or octonion n-space).…”