Lie groups and compact groups /:
The theory of Lie groups is a very active part of mathematics and it is the twofold aim of these notes to provide a self-contained introduction to the subject and to make results about the structure of Lie groups and compact groups available to a wide audience. Particular emphasis is placed upon res...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [England] ; New York :
Cambridge University Press,
1977.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
25. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | The theory of Lie groups is a very active part of mathematics and it is the twofold aim of these notes to provide a self-contained introduction to the subject and to make results about the structure of Lie groups and compact groups available to a wide audience. Particular emphasis is placed upon results and techniques which explicate the interplay between a Lie group and its Lie algebra, and, in keeping with current trends, a coordinate-free notation is used. Much of the general theory is illustrated by examples and exercises involving specific Lie groups. |
| Beschreibung: | 1 online resource (ix, 177 pages) |
| Bibliographie: | Includes bibliographical references (pages 169-173) and index. |
| ISBN: | 9781107360860 1107360862 9780511600715 0511600712 |
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| 245 | 1 | 0 | |a Lie groups and compact groups / |c John F. Price. |
| 260 | |a Cambridge [England] ; |a New York : |b Cambridge University Press, |c 1977. | ||
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| 504 | |a Includes bibliographical references (pages 169-173) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a The theory of Lie groups is a very active part of mathematics and it is the twofold aim of these notes to provide a self-contained introduction to the subject and to make results about the structure of Lie groups and compact groups available to a wide audience. Particular emphasis is placed upon results and techniques which explicate the interplay between a Lie group and its Lie algebra, and, in keeping with current trends, a coordinate-free notation is used. Much of the general theory is illustrated by examples and exercises involving specific Lie groups. | ||
| 505 | 0 | |a Cover; Title; Copyright; Contents; Preface; Chapter 1 Analytic manifolds; 1. 1 Manifolds and differentiability; 1. 2 The tangent bundle; 1. 3 Vector fields; Notes; Exercises; Chapter 2 Lie groups and Lie algebras; 2. 1 Lie groups; 2. 2 The Lie algebra of a Lie group; 2. 3 Homomorphisms of Lie groups; 2. 4 The general linear group; Notes; Exercises; Chapter 3 The Campbell-Baker-Hausdorff formula; 3.1 The CBH formula for Lie algebras; 3. 2 The CBH formula for Lie groups; 3. 3 Closed subgroups; 3. 4 Simply connected Lie groups; Notes; Exercises; Chapter 4 The geometry of Lie groups | |
| 505 | 8 | |a 4.1 Riemannian manifolds4. 2 Invariant metrics on Lie groups; 4. 3 Geodesies on Lie groups; Notes; Exercises; Chapter 5 Lie subgroups and subalgebras; 5.1 Subgroups and subalgebras; 5. 2 Normal subgroups and ideals; Notes; Exercises; Chapter 6 Characterisations and structure of compact Lie Groups; 6.1 Compact groups and Lie groups; 6. 2 Linear Lie groups; 6. 3 Simple and semisimple Lie algebras; 6. 4 The structure of compact Lie groups; 6. 5 Compact connected groups; Notes; Exercises; Appendix A Abstract harmonic analysis; A. 1 Topological groups; A. 2 Representations; A. 3 Compact groups | |
| 505 | 8 | |a A. 4 The Haar integralBibliography; Index | |
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| 650 | 0 | |a Compact groups. |0 http://id.loc.gov/authorities/subjects/sh85029280 | |
| 650 | 6 | |a Groupes de Lie. | |
| 650 | 6 | |a Groupes compacts. | |
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| 650 | 7 | |a Groupes compacts. |2 ram | |
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| author | Price, John F. (John Frederick), 1943- |
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| contents | Cover; Title; Copyright; Contents; Preface; Chapter 1 Analytic manifolds; 1. 1 Manifolds and differentiability; 1. 2 The tangent bundle; 1. 3 Vector fields; Notes; Exercises; Chapter 2 Lie groups and Lie algebras; 2. 1 Lie groups; 2. 2 The Lie algebra of a Lie group; 2. 3 Homomorphisms of Lie groups; 2. 4 The general linear group; Notes; Exercises; Chapter 3 The Campbell-Baker-Hausdorff formula; 3.1 The CBH formula for Lie algebras; 3. 2 The CBH formula for Lie groups; 3. 3 Closed subgroups; 3. 4 Simply connected Lie groups; Notes; Exercises; Chapter 4 The geometry of Lie groups 4.1 Riemannian manifolds4. 2 Invariant metrics on Lie groups; 4. 3 Geodesies on Lie groups; Notes; Exercises; Chapter 5 Lie subgroups and subalgebras; 5.1 Subgroups and subalgebras; 5. 2 Normal subgroups and ideals; Notes; Exercises; Chapter 6 Characterisations and structure of compact Lie Groups; 6.1 Compact groups and Lie groups; 6. 2 Linear Lie groups; 6. 3 Simple and semisimple Lie algebras; 6. 4 The structure of compact Lie groups; 6. 5 Compact connected groups; Notes; Exercises; Appendix A Abstract harmonic analysis; A. 1 Topological groups; A. 2 Representations; A. 3 Compact groups A. 4 The Haar integralBibliography; Index |
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| indexdate | 2024-11-27T13:25:16Z |
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| spelling | Price, John F. (John Frederick), 1943- https://id.oclc.org/worldcat/entity/E39PCjBkCHJHJJQXyqhmdpM8hb http://id.loc.gov/authorities/names/n85198455 Lie groups and compact groups / John F. Price. Cambridge [England] ; New York : Cambridge University Press, 1977. 1 online resource (ix, 177 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 25 Includes bibliographical references (pages 169-173) and index. Print version record. The theory of Lie groups is a very active part of mathematics and it is the twofold aim of these notes to provide a self-contained introduction to the subject and to make results about the structure of Lie groups and compact groups available to a wide audience. Particular emphasis is placed upon results and techniques which explicate the interplay between a Lie group and its Lie algebra, and, in keeping with current trends, a coordinate-free notation is used. Much of the general theory is illustrated by examples and exercises involving specific Lie groups. Cover; Title; Copyright; Contents; Preface; Chapter 1 Analytic manifolds; 1. 1 Manifolds and differentiability; 1. 2 The tangent bundle; 1. 3 Vector fields; Notes; Exercises; Chapter 2 Lie groups and Lie algebras; 2. 1 Lie groups; 2. 2 The Lie algebra of a Lie group; 2. 3 Homomorphisms of Lie groups; 2. 4 The general linear group; Notes; Exercises; Chapter 3 The Campbell-Baker-Hausdorff formula; 3.1 The CBH formula for Lie algebras; 3. 2 The CBH formula for Lie groups; 3. 3 Closed subgroups; 3. 4 Simply connected Lie groups; Notes; Exercises; Chapter 4 The geometry of Lie groups 4.1 Riemannian manifolds4. 2 Invariant metrics on Lie groups; 4. 3 Geodesies on Lie groups; Notes; Exercises; Chapter 5 Lie subgroups and subalgebras; 5.1 Subgroups and subalgebras; 5. 2 Normal subgroups and ideals; Notes; Exercises; Chapter 6 Characterisations and structure of compact Lie Groups; 6.1 Compact groups and Lie groups; 6. 2 Linear Lie groups; 6. 3 Simple and semisimple Lie algebras; 6. 4 The structure of compact Lie groups; 6. 5 Compact connected groups; Notes; Exercises; Appendix A Abstract harmonic analysis; A. 1 Topological groups; A. 2 Representations; A. 3 Compact groups A. 4 The Haar integralBibliography; Index Lie groups. http://id.loc.gov/authorities/subjects/sh85076786 Compact groups. http://id.loc.gov/authorities/subjects/sh85029280 Groupes de Lie. Groupes compacts. MATHEMATICS Algebra Linear. bisacsh Compact groups fast Lie groups fast Lie-groepen. gtt Topologische groepen. gtt Lie, Groupes de. ram Groupes compacts. ram Print version: Price, John F. (John Frederick), 1943- Lie groups and compact groups. Cambridge [Eng.] ; New York : Cambridge University Press, 1977 0521213401 (DLC) 76014034 (OCoLC)2597532 London Mathematical Society lecture note series ; 25. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552424 Volltext |
| spellingShingle | Price, John F. (John Frederick), 1943- Lie groups and compact groups / London Mathematical Society lecture note series ; Cover; Title; Copyright; Contents; Preface; Chapter 1 Analytic manifolds; 1. 1 Manifolds and differentiability; 1. 2 The tangent bundle; 1. 3 Vector fields; Notes; Exercises; Chapter 2 Lie groups and Lie algebras; 2. 1 Lie groups; 2. 2 The Lie algebra of a Lie group; 2. 3 Homomorphisms of Lie groups; 2. 4 The general linear group; Notes; Exercises; Chapter 3 The Campbell-Baker-Hausdorff formula; 3.1 The CBH formula for Lie algebras; 3. 2 The CBH formula for Lie groups; 3. 3 Closed subgroups; 3. 4 Simply connected Lie groups; Notes; Exercises; Chapter 4 The geometry of Lie groups 4.1 Riemannian manifolds4. 2 Invariant metrics on Lie groups; 4. 3 Geodesies on Lie groups; Notes; Exercises; Chapter 5 Lie subgroups and subalgebras; 5.1 Subgroups and subalgebras; 5. 2 Normal subgroups and ideals; Notes; Exercises; Chapter 6 Characterisations and structure of compact Lie Groups; 6.1 Compact groups and Lie groups; 6. 2 Linear Lie groups; 6. 3 Simple and semisimple Lie algebras; 6. 4 The structure of compact Lie groups; 6. 5 Compact connected groups; Notes; Exercises; Appendix A Abstract harmonic analysis; A. 1 Topological groups; A. 2 Representations; A. 3 Compact groups A. 4 The Haar integralBibliography; Index Lie groups. http://id.loc.gov/authorities/subjects/sh85076786 Compact groups. http://id.loc.gov/authorities/subjects/sh85029280 Groupes de Lie. Groupes compacts. MATHEMATICS Algebra Linear. bisacsh Compact groups fast Lie groups fast Lie-groepen. gtt Topologische groepen. gtt Lie, Groupes de. ram Groupes compacts. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85076786 http://id.loc.gov/authorities/subjects/sh85029280 |
| title | Lie groups and compact groups / |
| title_auth | Lie groups and compact groups / |
| title_exact_search | Lie groups and compact groups / |
| title_full | Lie groups and compact groups / John F. Price. |
| title_fullStr | Lie groups and compact groups / John F. Price. |
| title_full_unstemmed | Lie groups and compact groups / John F. Price. |
| title_short | Lie groups and compact groups / |
| title_sort | lie groups and compact groups |
| topic | Lie groups. http://id.loc.gov/authorities/subjects/sh85076786 Compact groups. http://id.loc.gov/authorities/subjects/sh85029280 Groupes de Lie. Groupes compacts. MATHEMATICS Algebra Linear. bisacsh Compact groups fast Lie groups fast Lie-groepen. gtt Topologische groepen. gtt Lie, Groupes de. ram Groupes compacts. ram |
| topic_facet | Lie groups. Compact groups. Groupes de Lie. Groupes compacts. MATHEMATICS Algebra Linear. Compact groups Lie groups Lie-groepen. Topologische groepen. Lie, Groupes de. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552424 |
| work_keys_str_mv | AT pricejohnf liegroupsandcompactgroups |