On Pappus' configuration in non-commutative projective geometry (Q5943037)

Let \(\pi\) be a finite dimensional projective space over a skewfield \(K\). If \(K\) is non-commutative, then the Pappus configuration does not close in general. Given three points on a line \(s\), and two points on another line \(r\), the author studies the set of points on \(r\) such that the Pappus configuration does close. It turns out that this set is a projective subline of \(r\) over a suitable subfield of \(K.\) It is also the set of fixed points of a certain projectivity. Conversely, many projectivities have such set as sets of fixed points.