Lie Groups Beyond an Introduction:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1996
|
| Schriftenreihe: | Progress in Mathematics
140 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Lie Groups Beyond an Introduction takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. A feature of the presentation is that it encourages the reader's comprehension of Lie group theory to evolve from beginner to expert: initial insights make use of actual matrices, while later insights come from such structural features as properties of root systems, or relationships among subgroups, or patterns among different subgroups. Topics include a description of all simply connected Lie groups in terms of semisimple Lie groups and semidirect products, the Cartan theory of complex semisimple Lie algebras, the Cartan-Weyl theory of the structure and representations of compact Lie groups and representations of complex semisimple Lie algebras, the classification of real semisimple Lie algebras, the structure theory of noncompact reductive Lie groups as it is now used in research, and integration on reductive groups. Many problems, tables, and bibliographical notes complete this comprehensive work, making the text suitable either for self-study or for courses in the second year of graduate study and beyond |
| Beschreibung: | 1 Online-Ressource (XV, 608 p) |
| ISBN: | 9781475724530 9781475724554 |
| DOI: | 10.1007/978-1-4757-2453-0 |
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| discipline | Mathematik |
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| format | Electronic eBook |
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| isbn | 9781475724530 9781475724554 |
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| spelling | Knapp, Anthony W. Verfasser aut Lie Groups Beyond an Introduction by Anthony W. Knapp Boston, MA Birkhäuser Boston 1996 1 Online-Ressource (XV, 608 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 140 Lie Groups Beyond an Introduction takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. A feature of the presentation is that it encourages the reader's comprehension of Lie group theory to evolve from beginner to expert: initial insights make use of actual matrices, while later insights come from such structural features as properties of root systems, or relationships among subgroups, or patterns among different subgroups. Topics include a description of all simply connected Lie groups in terms of semisimple Lie groups and semidirect products, the Cartan theory of complex semisimple Lie algebras, the Cartan-Weyl theory of the structure and representations of compact Lie groups and representations of complex semisimple Lie algebras, the classification of real semisimple Lie algebras, the structure theory of noncompact reductive Lie groups as it is now used in research, and integration on reductive groups. Many problems, tables, and bibliographical notes complete this comprehensive work, making the text suitable either for self-study or for courses in the second year of graduate study and beyond Mathematics Algebra Group theory Topological Groups Group Theory and Generalizations Topological Groups, Lie Groups Mathematik Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 s 1\p DE-604 Lie-Gruppe (DE-588)4035695-4 s 2\p DE-604 https://doi.org/10.1007/978-1-4757-2453-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Knapp, Anthony W. Lie Groups Beyond an Introduction Mathematics Algebra Group theory Topological Groups Group Theory and Generalizations Topological Groups, Lie Groups Mathematik Lie-Gruppe (DE-588)4035695-4 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4130355-6 |
| title | Lie Groups Beyond an Introduction |
| title_auth | Lie Groups Beyond an Introduction |
| title_exact_search | Lie Groups Beyond an Introduction |
| title_full | Lie Groups Beyond an Introduction by Anthony W. Knapp |
| title_fullStr | Lie Groups Beyond an Introduction by Anthony W. Knapp |
| title_full_unstemmed | Lie Groups Beyond an Introduction by Anthony W. Knapp |
| title_short | Lie Groups Beyond an Introduction |
| title_sort | lie groups beyond an introduction |
| topic | Mathematics Algebra Group theory Topological Groups Group Theory and Generalizations Topological Groups, Lie Groups Mathematik Lie-Gruppe (DE-588)4035695-4 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Mathematics Algebra Group theory Topological Groups Group Theory and Generalizations Topological Groups, Lie Groups Mathematik Lie-Gruppe Lie-Algebra |
| url | https://doi.org/10.1007/978-1-4757-2453-0 |
| work_keys_str_mv | AT knappanthonyw liegroupsbeyondanintroduction |