Matrix Groups: An Introduction to Lie Group Theory - Brossura

Baker, Andrew

Brossura

ISBN 10: 1852334703 ISBN 13: 9781852334703

Casa editrice: Springer, 2003

Riassunto

This book offers a first taste of the theory of Lie groups, focusing mainly on matrix groups: closed subgroups of real and complex general linear groups. The first part studies examples and describes classical families of simply connected compact groups. The second section introduces the idea of a lie group and explores the associated notion of a homogeneous space using orbits of smooth actions. The emphasis throughout is on accessibility.

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Recensione

"This excellent book gives an easy introduction to the theory of Lie groups and Lie algebras by restricting the material to real and complex matrix groups. This provides the reader not only with a wealth of examples, but it also makes the key concepts much more concrete. This combination makes the material in this book more easily accessible for the readers with a limited background...The book is very easy to read and suitable for an elementary course in Lie theory aimed at advanced undergraduates or beginning graduate students...To summarize, this is a well-written book, which is highly suited as an introductory text for beginning graduate students without much background in differential geometry or for advanced undergraduates. It is a welcome addition to the literature in Lie theory." --Mathematical Reviews

"This book is an introduction to Lie group theory with focus on the matrix case. ... This book can be recommended to students, making Lie group theory more accessible to them." --A. Akutowicz, Zentralblatt MATH, Vol. 1009, 2003

Contenuti

I. Basic Ideas and Examples.- 1. Real and Complex Matrix Groups.- 2. Exponentials, Differential Equations and One-parameter Subgroups.- 3. Tangent Spaces and Lie Algebras.- 4. Algebras, Quaternions and Quaternionic Symplectic Groups.- 5. Clifford Algebras and Spinor Groups.- 6. Lorentz Groups.- II. Matrix Groups as Lie Groups.- 7. Lie Groups.- 8. Homogeneous Spaces.- 9. Connectivity of Matrix Groups.- III. Compact Connected Lie Groups and their Classification.- 10. Maximal Tori in Compact Connected Lie Groups.- 11. Semi-simple Factorisation.- 12. Roots Systems, Weyl Groups and Dynkin Diagrams.- Hints and Solutions to Selected Exercises.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2003
• Lingua: Inglese
• ISBN 10: 1852334703
• ISBN 13: 9781852334703
• Rilegatura: Copertina flessibile
• Numero di pagine: 344
• Contatto del produttore: non disponibile
• Persona responsabile: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Germania