Units in Skew Fields

by Ernst Kleinert

Overview

This book is devoted to a study of the unit groups of orders in skew fields, finite dimensional and central over the rational field; it thereby belongs to the field of noncommutative arithmetic. Its purpose is a synopsis of results and methods, including full proofs of the most important results. It is addressed to researchers in number theory and arithmetic groups.

Product Details

ISBN-13:	9783034895552
Publisher:	Birkhäuser Basel
Publication date:	10/29/2012
Series:	Progress in Mathematics , #186
Edition description:	Softcover reprint of the original 1st ed. 2000
Pages:	80
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

0 Basic Facts.- 1 Hey’s Theorem and Consequences.- 2 Siegel-Weyl Reduction Theory.- 3 The Tamagawa Number and the Volume of G(?)/G(?).- 3.1 Statement of the main result.- 3.2 Proof of 3.1.- 3.3 The volume of G(?)/G(?).- 4 The Size of—.- 4.1 Statement of results.- 4.2 Proofs.- 5 Margulis’ Finiteness Theorem.- 5.1 The Result.- 5.2 Amenable groups.- 5.3 Kazhdan’s property (T).- 5.4 Proof of 5.1; beginning.- 5.5 Interlude: parabolics and their opposites.- 5.6 Continuation of the proof.- 5.7 Contracting automorphisms and the Moore Ergodicity theorem.- 5.8 End of proof.- 5.9 Appendix on measure theory.- 6 A Zariski Dense and a Free Subgroup of—.- 7 An Example.- 8 Problems.- 8.1 Generators.- 8.2 The congruence problem.- 8.3 Betti numbers.- References.