On Group Spaces Defined by Semidirect Products of Groups

Abstract

Publisher Summary This chapter introduces the concept of a semidirect product space (SPS) induced by the “affine action” of a semidirect product of groups. It presents an application of SPS—a geometric version of Witt's cancellation theorem for quadratic forms over fields involving two geometric invariants that can be defined for a quadratic form. The chapter also describes that with respect to arbitrary group extensions natural questions of geometric type arise. J.Andre suggested to express the splitting of an extension in geometric terms that leads to characterize geometrically when a group space is a SPS. As in the characterization of split extensions derivations and inner derivations play an essential role, it might be interesting to study these objects from the geometric point of view.