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Jordan Algebras and Algebraic Groups (Classics in Mathematics)

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Jordan Algebras and Algebraic Groups (Classics in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

From the reviews: "This book presents an important and novel approach to Jordan algebras. [...] Springer's work will be of service to research workers familiar with linear algebraic groups who find they need to know something about Jordan algebras and will provide Jordan algebraists with new techniques and a new approach to finite-dimensional algebras over fields." American Scientist

About the Author

From the reviews: "This book presents an important and novel approach to Jordan algebras. Jordan algebras have come to play a role in many areas of mathematics, including Lie algebras and the geometry of Chevalley groups. Springer's work will be of service to research workers familiar with linear algebraic groups who find they need to know something about Jordan algebras and will provide Jordan algebraists with new techniques and a new approach to finite-dimensional algebras over fields." (American Scientist) "By placing the classification of Jordan algebras in the perspective of classification of certain root systems, the book demonstrates that the structure theories associative, Lie, and Jordan algebras are not separate creations but rather instances of the one all-encompassing miracle of root systems. ..." (Math. Reviews)

Table of Contents

Preliminaries.- J-structures.- Examples.- The Quadratic Map of a J-structure.- The Lie Algebras Associates with a J-structure.- J-structures of Low Degree.- Relation with Jordan Algebras.- Relation with Quadratic Jordan Algebras.- The Minimum Polynomial of an Element.- Ideals, the Radical.- Peirce Decomposition Defined by an Idempotent Element.- Classification of Certain Algebraic Groups. Strongly Simple J-structures.- Simple J-structures.- The Structure Group of a Simple J-structure and the Related Lie Algebras.- Rationality Questions.

Product Details

ISBN:
9783540636328
Author:
Springer, Tony A.
Author:
Springer, T. A.
Author:
Springer, Tonny A.
Author:
Springer, T. A.
Publisher:
Springer
Location:
Berlin ;
Subject:
Algebra - General
Subject:
Group Theory
Subject:
Jordan algebras
Subject:
Linear algebraic groups
Subject:
Non-associative Rings and Algebras
Subject:
Group Theory and Generalizations
Subject:
Algebra - Abstract
Subject:
Mathematics - Algebra
Copyright:
Edition Description:
Reprint of the 1st ed. Berlin, Heidelberg, New York 1973.
Series:
Classics in Mathematics,
Publication Date:
19971211
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
181
Dimensions:
235 x 155 mm 287 gr

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Jordan Algebras and Algebraic Groups (Classics in Mathematics) New Trade Paper
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Product details 181 pages Springer-Verlag - English 9783540636328 Reviews:
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