Lie Groups, Lie Algebras, and Representations: An Elementary Introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2003
|
| Schriftenreihe: | Graduate Texts in Mathematics
222 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way that minimizes the amount of manifold theory needed. Thus, I neither assume a prior course on differentiable manifolds nor provide a con densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory. The standard books on Lie theory begin immediately with the general case: a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time |
| Beschreibung: | 1 Online-Ressource (XIV, 354 p) |
| ISBN: | 9780387215549 9781441923134 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-0-387-21554-9 |
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| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-0-387-21554-9 |
| format | Electronic eBook |
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| isbn | 9780387215549 9781441923134 |
| issn | 0072-5285 |
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| spelling | Hall, Brian C. Verfasser aut Lie Groups, Lie Algebras, and Representations An Elementary Introduction by Brian C. Hall New York, NY Springer New York 2003 1 Online-Ressource (XIV, 354 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 222 0072-5285 This book provides an introduction to Lie groups, Lie algebras, and repre sentation theory, aimed at graduate students in mathematics and physics. Although there are already several excellent books that cover many of the same topics, this book has two distinctive features that I hope will make it a useful addition to the literature. First, it treats Lie groups (not just Lie alge bras) in a way that minimizes the amount of manifold theory needed. Thus, I neither assume a prior course on differentiable manifolds nor provide a con densed such course in the beginning chapters. Second, this book provides a gentle introduction to the machinery of semi simple groups and Lie algebras by treating the representation theory of SU(2) and SU(3) in detail before going to the general case. This allows the reader to see roots, weights, and the Weyl group "in action" in simple cases before confronting the general theory. The standard books on Lie theory begin immediately with the general case: a smooth manifold that is also a group. The Lie algebra is then defined as the space of left-invariant vector fields and the exponential mapping is defined in terms of the flow along such vector fields. This approach is undoubtedly the right one in the long run, but it is rather abstract for a reader encountering such things for the first time Mathematics Group theory Topological Groups Mathematical physics Group Theory and Generalizations Topological Groups, Lie Groups Mathematical Methods in Physics Mathematik Mathematische Physik Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 s Lie-Algebra (DE-588)4130355-6 s Darstellungstheorie (DE-588)4148816-7 s 1\p DE-604 https://doi.org/10.1007/978-0-387-21554-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hall, Brian C. Lie Groups, Lie Algebras, and Representations An Elementary Introduction Mathematics Group theory Topological Groups Mathematical physics Group Theory and Generalizations Topological Groups, Lie Groups Mathematical Methods in Physics Mathematik Mathematische Physik Lie-Gruppe (DE-588)4035695-4 gnd Darstellungstheorie (DE-588)4148816-7 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4148816-7 (DE-588)4130355-6 |
| title | Lie Groups, Lie Algebras, and Representations An Elementary Introduction |
| title_auth | Lie Groups, Lie Algebras, and Representations An Elementary Introduction |
| title_exact_search | Lie Groups, Lie Algebras, and Representations An Elementary Introduction |
| title_full | Lie Groups, Lie Algebras, and Representations An Elementary Introduction by Brian C. Hall |
| title_fullStr | Lie Groups, Lie Algebras, and Representations An Elementary Introduction by Brian C. Hall |
| title_full_unstemmed | Lie Groups, Lie Algebras, and Representations An Elementary Introduction by Brian C. Hall |
| title_short | Lie Groups, Lie Algebras, and Representations |
| title_sort | lie groups lie algebras and representations an elementary introduction |
| title_sub | An Elementary Introduction |
| topic | Mathematics Group theory Topological Groups Mathematical physics Group Theory and Generalizations Topological Groups, Lie Groups Mathematical Methods in Physics Mathematik Mathematische Physik Lie-Gruppe (DE-588)4035695-4 gnd Darstellungstheorie (DE-588)4148816-7 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Mathematics Group theory Topological Groups Mathematical physics Group Theory and Generalizations Topological Groups, Lie Groups Mathematical Methods in Physics Mathematik Mathematische Physik Lie-Gruppe Darstellungstheorie Lie-Algebra |
| url | https://doi.org/10.1007/978-0-387-21554-9 |
| work_keys_str_mv | AT hallbrianc liegroupsliealgebrasandrepresentationsanelementaryintroduction |