Units in Skew Fields

Ernst Kleinert (Autor)

Buch | Softcover

VIII, 80 Seiten

2012
Springer Basel (Verlag)
978-3-0348-9555-2 (ISBN)

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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.

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.

Erscheint lt. Verlag	29.10.2012
Reihe/Serie	Progress in Mathematics
Zusatzinfo	VIII, 80 p.
Verlagsort	Basel
Sprache	englisch
Maße	155 x 235 mm
Gewicht	157 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Medizin / Pharmazie
Schlagworte	Algebra • arithmetic • commutative property • Geometrie • Gruppentheorie • Number Theory • Zahlentheorie
ISBN-10	3-0348-9555-0 / 3034895550
ISBN-13	978-3-0348-9555-2 / 9783034895552
Zustand	Neuware