Differential Geometry, Lie Groups, and Symmetric Spaces

Sigurdur Helgason

640 pages, parution le 17/12/2001

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Résumé

The study of homogeneous spaces provides excellent insights into both differential geometry and Lie groups. In geometry, for instance, general theorems and properties will also hold for homogeneous spaces, and will usually be easier to understand and to prove in this setting. For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason's classic Differential Geometry, Lie Groups, and Symmetric Spaces has been--and continues to be--the standard source for this material.

Helgason begins with a concise, self-contained introduction to differential geometry. He then introduces Lie groups and Lie algebras, including important results on their structure. This sets the stage for the introduction and study of symmetric spaces, which form the central part of the book. The text concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras and Cartan's classification of simple Lie algebras .

The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All the problems have either solutions or substantial hints, found at the back of the book.

For this latest edition, Helgason has made corrections and added helpful notes and useful references. The sequels to the present book are published in the AMS's Mathematical Surveys and Monographs Series: Groups and Geometric Analysis, Volume 83, and Geometric Analysis on Symmetric Spaces, Volume 39.

Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis.

Contents

Elementary differential geometry
Lie groups and Lie algebras
Structure of semisimple Lie algebras
Symmetric spaces
Decomposition of symmetric spaces
Symmetric spaces of the noncompact type
Symmetric spaces of the compact type
Hermitian symmetric spaces
Structure of semisimple Lie groups
The classification of simple Lie algebras and of symmetric spaces
Solutions to exercises
Some details
Bibliography
List of notational conventions
Symbols frequently used
Index
Reviews for the first edition

L'auteur - Sigurdur Helgason

Sigurdur Helgason was awarded the Steele Prize for Groups and Geometric Analysis and the companion volume, Differential Geometry, Lie Groups and Symmetric Spaces.

Caractéristiques techniques

	PAPIER
Éditeur(s)	American Mathematical Society (AMS)
Auteur(s)	Sigurdur Helgason
Parution	17/12/2001
Nb. de pages	640
Format	18 x 26
Couverture	Relié
Poids	1350g
Intérieur	Noir et Blanc
EAN13	9780821828489
ISBN13	978-0-8218-2848-9