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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.
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.
- 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
| Erscheinungsjahr: | 2006 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 276 |
| ISBN-13: | 9780199202515 |
| ISBN-10: | 0199202516 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Rossmann, Wulf |
| Hersteller: | OUP Oxford |
| Maße: | 234 x 156 x 15 mm |
| Von/Mit: | Wulf Rossmann |
| Erscheinungsdatum: | 29.06.2006 |
| Gewicht: | 0,424 kg |
- 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
| Erscheinungsjahr: | 2006 |
|---|---|
| Fachbereich: | Arithmetik & Algebra |
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Seiten: | 276 |
| ISBN-13: | 9780199202515 |
| ISBN-10: | 0199202516 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Rossmann, Wulf |
| Hersteller: | OUP Oxford |
| Maße: | 234 x 156 x 15 mm |
| Von/Mit: | Wulf Rossmann |
| Erscheinungsdatum: | 29.06.2006 |
| Gewicht: | 0,424 kg |
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