ENGLISH

Finite-dimensional division algebras over fields

By Nathan Jacobson

Book information

Publisher
Springer
Year
1996
ISBN
3540570292, 9783540570295
LCC
QA247.45 .J33 1996
Open Library ID
OL993122M
Language
english
Format
DJVU
Filesize
2 MB (2299848 bytes)
Series
Grundlehren Der Mathematischen Wissenschaften
Edition
1st ed. 1996. Corr. 2nd printing
Pages
290\290
Topic
Mathematics Algebra
Library
Kolxo3
DPI
600
Scanned
yes
Time added
2010-07-29 05:14:56

Description

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

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