Lie Groups: An Introduction through Linear Groups (Oxford Graduate Texts in Mathematics) - Couverture souple

Rossmann, Wulf

Couverture souple

ISBN 10 : 0199202516 ISBN 13 : 9780199202515

Editeur : Oxford University Press, USA, 2006

Synopsis

This book is an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analyzed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, root, weights and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur's lemma and its consequences, and proceeds from there to the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.

A propos du livre

Présentation de l'éditeur

Lie Groups is intended as an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject starting from basic undergraduate mathematics. The correspondence between linear Lie groups and Lie algebras is developed in its local and global aspects. The classical groups are analysed in detail, first with elementary matrix methods, then with the help of the structural tools typical of the theory of semisimple groups, such as Cartan subgroups, roots, weights, and reflections. The fundamental groups of the classical groups are worked out as an application of these methods. Manifolds are introduced when needed, in connection with homogeneous spaces, and the elements of differential and integral calculus on manifolds are presented, with special emphasis on integration on groups and homogeneous spaces. Representation theory starts from first principles, such as Schur's lemma and its consequences, and proceeds from there to the Peter-Weyl theorem, Weyl's character formula, and the Borel-Weil theorem, all in the context of linear groups.

Revue de presse

'A nice feature of this book is a variety of problems proposed at the end of each section; this makes it especially suitable as a textbook for a first course in Lie groups, addressed to an audience of mathematicians or physicists. MMA Reviews, March 2007, Fabio Mainardi

Détails de l'édition

• Éditeur: Oxford University Press, USA
• Date d'édition: 2006
• Langue: anglais
• ISBN 10: 0199202516
• ISBN 13: 9780199202515
• Reliure: Broché
• Nombre de pages: 265
• Coordonnées du fabricant: non disponible
• Personne responsable: Ufficio Anagrafiche Messaggerie; ufficio.anagrafiche@meli.it; ; Via Verdi, 8; Assago Milano; 20090; Italie