Finite-Dimensional Division Algebras over Fields

Nathan Jacobson (Autor)

Buch | Softcover

VIII, 284 Seiten

2014 | 1. Softcover reprint of the original 1st ed. 1996
Springer Berlin (Verlag)
978-3-662-30883-7 (ISBN)

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These algebras determine, by the Sliedderburn Theorem. the semi-simple finite dimensional algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brauer-Severi varieties. Sie shall be interested in these algebras which have an involution. Algebras with involution arose first in the study of the so-called .'multiplication algebras of Riemann matrices". Albert undertook their study at the behest of Lefschetz. He solved the problem of determining these algebras. The problem has an algebraic part and an arithmetic part which can be solved only by determining the finite dimensional simple algebras over an algebraic number field. We are not going to consider the arithmetic part but will be interested only in the algebraic part. In Albert's classical book (1939). both parts are treated. A quick survey of our Table of Contents will indicate the scope of the present volume. The largest part of our book is the fifth chapter which deals with invo- torial rimple algebras of finite dimension over a field. Of particular interest are the Jordan algebras determined by these algebras with involution. Their structure is determined and two important concepts of these algebras with involution are the universal enveloping algebras and the reduced norm. Of great importance is the concept of isotopy. There are numerous applications of these concepts, some of which are quite old.

Skew Polynomials and Division Algebras.- Brauer Factor Sets and Noether Factor Sets.- Galois Descent and Generic Splitting Fields.- p-Algebras.- Simple Algebras with Involution.

"...the author takes us on a tour of division algebras, pointing out the salient facts, often with little-known proofs, but never going on so long as to bore the reader. This makes the book a pleasure to read" Bulletin of the London Mathematical Society

Erscheint lt. Verlag	23.8.2014
Zusatzinfo	VIII, 284 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	440 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Schlagworte	Algebra • associative ring • Associative Rings • Commutative Ring • Commutative Rings • Field • matrices • Nonassociative • polynomial • Ring • Ring Theory
ISBN-10	3-662-30883-5 / 3662308835
ISBN-13	978-3-662-30883-7 / 9783662308837
Zustand	Neuware