THE SKEW-HYPERBOLIC MOTION GROUP OF THE QUATERNION PLANE

Up to conjugation, there exist three different polarities of the proje ctive plane P2H over Hamilton's quaternions H. The skew hyperbolic mot ion group of P2H is introduced as the centralizer of a polarity ''of t he third kind''. According to a result of R. Lowen, the quaternion pla ne is characterized among the eight-dimensional stable planes by the f act that it admits an effective action of the centralizer of a polarit y of the first or second kind (i.e., the elliptic or the hyperbolic mo tion group). In the present paper, we prove the analogous result for t he skew hyperbolic case.