Jordan Algebras and Algebraic Groups

Tonny A. Springer

168 pages, parution le 01/01/1997

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Résumé

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)

Contents

Preliminaries 1

1 J-structures 9
2 Examples 23
3 The Quadratic Map of a J-structure 39
4 The Lie Algebras Associated with a J-structure 48
5 J-structures of Low Degree 54
6 Relation with Jordan Algebras (Characteristic [actual symbol not reproducible] 2) 66
7 Relation with Quadratic Jordan Algebras 72
8 The Minimum Polynomial of an Element 79
9 Ideals, the Radical 83
10 Peirce Decomposition Defined by an Idempotent Element 90
11 Classification of Certain Algebraic Groups 106
12 Strongly Simple J-structures 122
13 Simple J-structures 128
14 The Structure Group of a Simple J-structure and the Related Lie Algebras 136
15 Rationality Questions 158

Bibliography 167
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Tonny A. Springer
Parution	01/01/1997
Nb. de pages	168
Format	15,5 x 23,5
Couverture	Broché
Poids	297g
Intérieur	Noir et Blanc
EAN13	9783540636328