ENGLISH

Finite-Dimensional Division Algebras over Fields

By Nathan Jacobson (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1996
ISBN
3540570292, 9783540570295
DOI
10.1007/978-3-642-02429-0
LCC
QA247.45 .J33 1996
Open Library ID
OL993122M
Language
english
Format
PDF
Filesize
25 MB (25743889 bytes)
Series
Grundlehren Der Mathematischen Wissenschaften
Edition
1
Pages
284\290
Topic
Mathematics Algebra
Scanned
yes
Time added
2011-04-28 18:43:47
Algebra

Description

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).

Similar books