Finite-dimensional division algebras over fields

✍ Scribed by Nathan Jacobson

• Publisher: Springer
• Year: 1996
• Tongue: English
• Leaves: 290
• Series: Grundlehren Der Mathematischen Wissenschaften
• Edition: 1st ed. 1996. Corr. 2nd printing
• Category: Library

✦ Synopsis

Finite-Dimensional Division Algebras over fields determine, by the Wedderburn 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. 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 involutorial 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

3540570292......Page 1
Finite-Dimensional\rDivision Algebras\rover Fields......Page 3
PREFACE......Page 5
Table of Contents......Page 6
I. Skew Polynomials and Division Algebras......Page 8
11. Brauer Factor Sets and Noether Factor\rSets......Page 48
111. Galois Descent and Generic Splitting\rFields......Page 102
IV. p-Algebras\rA......Page 161
V. Simple Algebras with Involution......Page 192
References......Page 282