Lie Groups: An Introduction through Linear Groups (Oxford Graduate Texts in Mathematics): 5 - Brossura

Rossmann, Wulf

Brossura

ISBN 10: 0199202516 ISBN 13: 9780199202515

Casa editrice: Oxford University Press, USA, 2006

Riassunto

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.

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Recensione

'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

L'autore

Wulf Rossmann is in the Department of Mathematics and Statistics, University of Ottawa.

Dettagli dell'edizione

• Editore: Oxford University Press, USA
• Data di pubblicazione: 2006
• Lingua: Inglese
• ISBN 10: 0199202516
• ISBN 13: 9780199202515
• Rilegatura: Copertina flessibile
• Numero di pagine: 276
• Contatto del produttore: non disponibile
• Persona responsabile: Ufficio Anagrafiche Messaggerie; ufficio.anagrafiche@meli.it; ; Via Verdi, 8.; Assago Milano; 20090; Italia