Lie Theory: Lie Algebras and Representations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
2004
|
| Schriftenreihe: | Progress in Mathematics
228 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title Lie Theory, feature survey work and original results by well-established researchers in key areas of semisimple Lie theory. A wide spectrum of topics is treated, with emphasis on the interplay between representation theory and the geometry of adjoint orbits for Lie algebras over fields of possibly finite characteristic, as well as for infinite-dimensional Lie algebras. Also covered is unitary representation theory and branching laws for reductive subgroups, an active part of modern representation theory. Finally, there is a thorough discussion of compactifications of symmetric spaces, and harmonic analysis through a far-reaching generalization of Harish--Chandra's Plancherel formula for semisimple Lie groups. Ideal for graduate students and researchers, Lie Theory provides a broad, clearly focused examination of semisimple Lie groups and their integral importance to research in many branches of mathematics. Lie Theory: Lie Algebras and Representations contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." Both are comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations |
| Beschreibung: | 1 Online-Ressource (XI, 331 p) |
| ISBN: | 9780817681920 9781461264835 |
| DOI: | 10.1007/978-0-8176-8192-0 |
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| 500 | |a Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title Lie Theory, feature survey work and original results by well-established researchers in key areas of semisimple Lie theory. A wide spectrum of topics is treated, with emphasis on the interplay between representation theory and the geometry of adjoint orbits for Lie algebras over fields of possibly finite characteristic, as well as for infinite-dimensional Lie algebras. Also covered is unitary representation theory and branching laws for reductive subgroups, an active part of modern representation theory. Finally, there is a thorough discussion of compactifications of symmetric spaces, and harmonic analysis through a far-reaching generalization of Harish--Chandra's Plancherel formula for semisimple Lie groups. Ideal for graduate students and researchers, Lie Theory provides a broad, clearly focused examination of semisimple Lie groups and their integral importance to research in many branches of mathematics. Lie Theory: Lie Algebras and Representations contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." Both are comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations | ||
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Jantzen, Jens Carsten |
| author_facet | Jantzen, Jens Carsten |
| author_role | aut |
| author_sort | Jantzen, Jens Carsten |
| author_variant | j c j jc jcj |
| building | Verbundindex |
| bvnumber | BV042419202 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)725155976 (DE-599)BVBBV042419202 |
| dewey-full | 512.482 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.482 512.55 |
| dewey-search | 512.482 512.55 |
| dewey-sort | 3512.482 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-0-8176-8192-0 |
| format | Electronic eBook |
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| isbn | 9780817681920 9781461264835 |
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| spelling | Jantzen, Jens Carsten Verfasser aut Lie Theory Lie Algebras and Representations by Jens Carsten Jantzen, Karl-Hermann Neeb ; edited by Jean-Philippe Anker, Bent Orsted Boston, MA Birkhäuser Boston 2004 1 Online-Ressource (XI, 331 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 228 Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title Lie Theory, feature survey work and original results by well-established researchers in key areas of semisimple Lie theory. A wide spectrum of topics is treated, with emphasis on the interplay between representation theory and the geometry of adjoint orbits for Lie algebras over fields of possibly finite characteristic, as well as for infinite-dimensional Lie algebras. Also covered is unitary representation theory and branching laws for reductive subgroups, an active part of modern representation theory. Finally, there is a thorough discussion of compactifications of symmetric spaces, and harmonic analysis through a far-reaching generalization of Harish--Chandra's Plancherel formula for semisimple Lie groups. Ideal for graduate students and researchers, Lie Theory provides a broad, clearly focused examination of semisimple Lie groups and their integral importance to research in many branches of mathematics. Lie Theory: Lie Algebras and Representations contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." Both are comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations Mathematics Algebra Group theory Topological Groups Harmonic analysis Geometry Number theory Topological Groups, Lie Groups Group Theory and Generalizations Abstract Harmonic Analysis Number Theory Mathematik Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Halbeinfache Lie-Gruppe (DE-588)4122188-6 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf 1\p (DE-588)4056995-0 Statistik gnd-content Lie-Algebra (DE-588)4130355-6 s Darstellungstheorie (DE-588)4148816-7 s 2\p DE-604 Halbeinfache Lie-Gruppe (DE-588)4122188-6 s 3\p DE-604 Neeb, Karl-Hermann Sonstige oth Anker, Jean-Philippe Sonstige oth Orsted, Bent Sonstige oth https://doi.org/10.1007/978-0-8176-8192-0 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jantzen, Jens Carsten Lie Theory Lie Algebras and Representations Mathematics Algebra Group theory Topological Groups Harmonic analysis Geometry Number theory Topological Groups, Lie Groups Group Theory and Generalizations Abstract Harmonic Analysis Number Theory Mathematik Darstellungstheorie (DE-588)4148816-7 gnd Halbeinfache Lie-Gruppe (DE-588)4122188-6 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4148816-7 (DE-588)4122188-6 (DE-588)4130355-6 (DE-588)4056995-0 |
| title | Lie Theory Lie Algebras and Representations |
| title_auth | Lie Theory Lie Algebras and Representations |
| title_exact_search | Lie Theory Lie Algebras and Representations |
| title_full | Lie Theory Lie Algebras and Representations by Jens Carsten Jantzen, Karl-Hermann Neeb ; edited by Jean-Philippe Anker, Bent Orsted |
| title_fullStr | Lie Theory Lie Algebras and Representations by Jens Carsten Jantzen, Karl-Hermann Neeb ; edited by Jean-Philippe Anker, Bent Orsted |
| title_full_unstemmed | Lie Theory Lie Algebras and Representations by Jens Carsten Jantzen, Karl-Hermann Neeb ; edited by Jean-Philippe Anker, Bent Orsted |
| title_short | Lie Theory |
| title_sort | lie theory lie algebras and representations |
| title_sub | Lie Algebras and Representations |
| topic | Mathematics Algebra Group theory Topological Groups Harmonic analysis Geometry Number theory Topological Groups, Lie Groups Group Theory and Generalizations Abstract Harmonic Analysis Number Theory Mathematik Darstellungstheorie (DE-588)4148816-7 gnd Halbeinfache Lie-Gruppe (DE-588)4122188-6 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Mathematics Algebra Group theory Topological Groups Harmonic analysis Geometry Number theory Topological Groups, Lie Groups Group Theory and Generalizations Abstract Harmonic Analysis Number Theory Mathematik Darstellungstheorie Halbeinfache Lie-Gruppe Lie-Algebra Statistik |
| url | https://doi.org/10.1007/978-0-8176-8192-0 |
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