Finite-Dimensional Division Algebras over Fields / Edition 1

Finite-Dimensional Division Algebras over Fields / Edition 1

by Nathan Jacobson
     
 

ISBN-10: 3540570292

ISBN-13: 9783540570295

Pub. Date: 01/01/2010

Publisher: Springer Berlin Heidelberg

Finite-dimensional division algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensio= nal algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brau= er-Severi varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many

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Overview

Finite-dimensional division algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensio= nal algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brau= er-Severi varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts;they arose first in the study of the so-called "multiplication algebras of Riemann matrices". The largest part of the book is the fifth chapter, dealing with involu= torial simple algebras of finite dimension over a field. Of particular interest are the Jordan algebras determined by these algebras with involution;their structure is discussed. Two important concepts of these algebras with involution are the universal enveloping algebras and the reduced norm.

Corrections of the 1st edition (1996) carried out on behalf of N. Jacobson (deceased) by Prof. P.M. Cohn (UC London, UK).

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Product Details

ISBN-13:
9783540570295
Publisher:
Springer Berlin Heidelberg
Publication date:
01/01/2010
Edition description:
1st ed. 1996. Corr. 2nd printing 2009
Pages:
286
Product dimensions:
9.21(w) x 6.14(h) x 0.69(d)

Table of Contents

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

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