Introduction to Lie algebras
Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. Based on a lecture course given to fourth-year undergraduates, this book provides an elementary introduction to Lie algebras. It...
保存先:
| 主要な著者: | , |
|---|---|
| フォーマット: | Livre numérique |
| 言語: | Anglais |
| 出版事項: |
London :
Springer London
[20..].
Cham : Springer Nature |
| 版: | 1st ed. 2006. |
| シリーズ: | Springer Undergraduate Mathematics Series
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| 主題: | |
| オンライン･アクセス: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| 注記: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Introduction to Lie Algebras, Texte imprimé, 9781848004221 • Introduction to Lie algebras, Karin Erdmann and Mark J. Wildon, 2006, London, Springer, 1 volume (X-251 pages), Springer undergraduate mathematics series, 978-1-84628-040-5 |
目次:
- Ideals and Homomorphisms Low-Dimensional Lie Algebras Solvable Lie Algebras and a Rough Classification Subalgebras of gl(V) Engel's Theorem and Lie's Theorem Some Representation Theory Representations of sl(2, C) Cartan's Criteria The Root Space Decomposition Root Systems The Classical Lie Algebras The Classification of Root Systems Simple Lie Algebras Further Directions Appendix A: Linear Algebra Appendix B: Weyl's Theorem Appendix C: Cartan Subalgebras Appendix D: Weyl Groups Appendix E: Answers to Selected Exercises.
- Ideals and Homomorphisms
- Low-Dimensional Lie Algebras
- Solvable Lie Algebras and a Rough Classification
- Subalgebras of gl(V)
- Engel s Theorem and Lie s Theorem
- Some Representation Theory
- Representations of sl(2, C)
- Cartan s Criteria
- The Root Space Decomposition
- Root Systems
- The Classical Lie Algebras
- The Classification of Root Systems
- Simple Lie Algebras
- Further Directions
- Appendix A: Linear Algebra
- Appendix B: Weyl s Theorem
- Appendix C: Cartan Subalgebras
- Appendix D: Weyl Groups
- Appendix E: Answers to Selected Exercises