Zur gruppentheoretischen Darstellung der projektiv-metrischen Geometrien

Abstract

The “extended reflection group” of a metric vector space was introduced by Nolte [10] to get a group theoretical representation of the corresponding protective metric geometry (in the sense of Schröder [12]). Nolte characterizes the extended. reflection, group among all representing groups if the characteristic of the underlying field is ≠ 2. We give a new proof of Nolte's result which does not depend on the characteristic. As a consequence we get that the “generated protective Clifford group” (see [12]) is isomorphic to the extended reflection group. Finally, we give examples of other representing groups.