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Algèbre: Chapitre 9: Formes Sesquilinéaires et Formes Quadratiques

N. Bourbaki
Publisher: 
Springer Verlag
Publication Date: 
2007
Number of Pages: 
209
Format: 
Paperback
Series: 
Éléments de Mathématique
Price: 
39.95
ISBN: 
9783540353386
Category: 
Monograph
[Reviewed by
Fernando Q. Gouvêa
, on
07/5/2007
]

Bourbaki's Éléments de Mathématique is probably one of the most famous — and most controversial — series of mathematics books ever published. The original French volumes were published by Hermann, but the series has now moved to Springer, which is reprinting them to make the complete set available.

This volume is an essentially unchanged reprint of chapter nine of Bourbaki's algebra, originally published in 1959; in fact, the only change I can detect is that the cover is now (of course) yellow. It treats the basic theory of bilinear and sesquilinear forms and the topics that arise naturally from them: quadratic and hermitian forms, the classical symplectic, orthogonal, and unitary groups, and Clifford algebras, for example.

It's nice to have these books back in print and easily available.


Fernando Q. Gouvêa is the editor of MAA Reviews and is Carter Professor of Mathematics at Colby College. He owns several Bourbaki volumes and subvolumes; he is happy to have this one, which was missing from his set.

1. Formes sesquilinéaires

2. Discriminant d'une forme sesquilinéaire

3. Formes hermitiennes et formes quadratiques

4. Sous-espaces totalement isotropes. Thèoreme de Witt

5. Propriétés spéciales aux formes bilinéaires alternées

6. Propriétés spéciales aux formes hermitiennes

7. Forms hermitiennes et corps ordonnés

8. Types de formes quadratiques

9. Algèbres de Clifford

10. Angles

 

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