The collineations which act as addition and multiplication on points in a certain class of projective Klingenberg planes

Abstract

Let be the projective Klingenberg plane coordinated by the dual quaternion ring where Q is any quaternion ring. In this paper, we determine the addition and multiplication of the points on the line of as the image of some collineations of the plane . To do this, we give the collineations and . Later we show that the addition and multiplication of the nonneighbor points on the line can be obtained as the images under that and .

MSC: 51C05, 51J10, 12E15.