Modulo (1,1) Periodicity of Clifford Algebras and Generalized (Anti-)Moebius Transformations

摘要

In the first chapter the reader meets a synoptic introduction in Clifford algebras and spin representations. A constructive method is given to determine the scalar products on the spinor spaces. Chapter 2 presents the author's theory of generalized (anti-)Mobius transformations, based on the modulo (1,1) periodicity of Clifford algebras. Chapter 3 is a reminiscence of Vahlen's paper. The hyperbolic group is seen to be covered by a subgroup of (anti-)Mobius transformations belonging to a positive definite vector space. Chapter 4 discusses the geometry of the Siegel domains of type four. The author's theory of (anti-)Mobius transformations, also valid for complex vector spaces, makes it possible to give a non-linear representation of the groups of biholomorphic self-mappings.