Finite-Dimensional Division Algebras over Fields

✍ Scribed by Nathan Jacobson (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1996
• Tongue: English
• Leaves: 290
• Series: Grundlehren der Mathematischen Wissenschaften
• Edition: 1
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Front Matter....Pages i-viii
Skew Polynomials and Division Algebras....Pages 1-40
Brauer Factor Sets and Noether Factor Sets....Pages 41-94
Galois Descent and Generic Splitting Fields....Pages 95-153
p-Algebras....Pages 154-184
Simple Algebras with Involution....Pages 185-274
Back Matter....Pages 275-283

✦ Subjects

Algebra