Lie Groups
An Introduction Through Linear Groups
Seiten
2006
Oxford University Press (Verlag)
978-0-19-920251-5 (ISBN)
Oxford University Press (Verlag)
978-0-19-920251-5 (ISBN)
This new in paperback edition provides a clear introduction to the theory of Lie groups and their representations for advanced undergraduates and graduate students in mathematics. Starting from basic undergraduate level mathematics, the text proceeds through the fundamentals of Lie theory up to topics in representation theory.
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.
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.
Preface ; 1. The exponential map ; 2. Lie theory ; 3. The classical groups ; 4. Manifolds, homogeneous spaces, Lie groups ; 5. Integration ; 6. Representations ; Appendix: Analytic Functions and Inverse Function Theorem ; References ; Index
| Erscheint lt. Verlag | 29.6.2006 |
|---|---|
| Reihe/Serie | Oxford Graduate Texts in Mathematics ; 5 |
| Verlagsort | Oxford |
| Sprache | englisch |
| Maße | 157 x 232 mm |
| Gewicht | 431 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| ISBN-10 | 0-19-920251-6 / 0199202516 |
| ISBN-13 | 978-0-19-920251-5 / 9780199202515 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Eine Einführung für Studienanfänger
Buch | Softcover (2025)
Springer Spektrum (Verlag)
CHF 41,95
Sieben ausgewählte Themenstellungen
Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
CHF 89,95
