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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Wahrscheinlichkeitstheorie & Statistik Quadratic and Hermitian Forms over Rings
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Quadratic and Hermitian Forms over Rings
Max-Albert Knus (Gebundene Ausgabe, Englisch)
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Beschreibung
From its birth (in Babylon?) till 1936 the theory of quadratic forms dealt almost exclusively with forms over the real field, the complex field or the ring of integers. Only as late as 1937 were the foundations of a theory over an arbitrary field laid. This was in a famous paper by Ernst Witt. Still too early, apparently, because it took another 25 years for the ideas of Witt to be pursued,… notably by Albrecht Pfister, and expanded into a full branch of algebra. Around 1960 the development of algebraic topology and algebraic K-theory led to the study of quadratic forms over commutative rings and hermitian forms over rings with involutions. Not surprisingly, in this more general setting, algebraic K-theory plays the role that linear algebra plays in the case of fields. This book exposes the theory of quadratic and hermitian forms over rings in a very general setting. It avoids, as far as possible, any restriction on the characteristic and takes full advantage of the functorial aspects of the theory. The advantage of doing so is not only aesthetical: on the one hand, some classical proofs gain in simplicity and transparency, the most notable examples being the results on low-dimensional spinor groups; on the other hand new results are obtained, which went unnoticed even for fields, as in the case of involutions on 16-dimensional central simple algebras. The first chapter gives an introduction to the basic definitions and properties of hermitian forms which are used throughout the book. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
05.04.1991
Sprache
Englisch
EAN
9783540521174
Herausgeber
Springer Berlin
Serien- oder Bandtitel
Grundlehren der mathematischen Wissenschaften
Sonderedition
Nein
Autor
Max-Albert Knus
Seitenanzahl
524
Einbandart
Gebundene Ausgabe
Bandzählung
294
Schlagwörter
tool, hermitian forms, Clifford algebras, algebraic K-theory, quadratic forms, Hermitesche Formen, Grad, Dimension, theorem, K-theory, Quadratische Algebra, algebraische K-Theorie, Clifford Algebren, Algebra, Quadratische Form
Thema-Inhalt
PBH - Zahlentheorie
PBMW - Algebraische Geometrie
Höhe
235 mm
Breite
15.5 cm
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