Cross ratios of points and lines in Moufang planes (Q2703561)

If \(M\) is a projective plane co-ordinated by an alternative field \(A\), \(\text{char} A\neq 2\), then \(M\) is Desarguesian if \(A\) is associative, and \(M\) is a Moufang plane if \(A\) is non-associative (so that \(A\) is a Cayley division algebra over its centre).NEWLINENEWLINENEWLINEIn this paper, the authors first extend the known definition of cross-ratio of collinear points to the whole Moufang plane and then introduce the concept of cross-ratio for lines. The known results about cross-ratios of points are then adapted to cross-ratios of lines without using the principle of duality. Finally a theorem relating the two is proved.