Infinite Dimensional Kähler Manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2001
|
| Schriftenreihe: | DMV Seminar Band
31 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Having been used mainly as a tool for the study of finite dimensional objects, the emphasis has changed and they are now frequently studied for their own independent interest. On the one hand this is a collection of closely related articles on infinite dimensional Kähler manifolds and associated group actions which grew out of a DMV-Seminar on the same subject. On the other hand it covers significantly more ground than was possible during the seminar in Oberwolfach and is in a certain sense intended as a systematic approach which ranges from the foundations of the subject to recent developments. It should be accessible to doctoral students and as well researchers coming from a wide range of areas. The initial chapters are devoted to a rather selfcontained introduction to group actions on complex and symplectic manifolds and to Borel-Weil theory in finite dimensions. These are followed by a treatment of the basics of infinite dimensional Lie groups, their actions and their representations. Finally, a number of more specialized and advanced topics are discussed, e.g., Borel-Weil theory for loop groups, aspects of the Virasoro algebra, (gauge) group actions and determinant bundles, and second quantization and the geometry of the infinite dimensional Grassmann manifold |
| Beschreibung: | 1 Online-Ressource (XIII, 375p) |
| ISBN: | 9783034882279 9783764366025 |
| DOI: | 10.1007/978-3-0348-8227-9 |
Internformat
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| 500 | |a Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Having been used mainly as a tool for the study of finite dimensional objects, the emphasis has changed and they are now frequently studied for their own independent interest. On the one hand this is a collection of closely related articles on infinite dimensional Kähler manifolds and associated group actions which grew out of a DMV-Seminar on the same subject. On the other hand it covers significantly more ground than was possible during the seminar in Oberwolfach and is in a certain sense intended as a systematic approach which ranges from the foundations of the subject to recent developments. It should be accessible to doctoral students and as well researchers coming from a wide range of areas. The initial chapters are devoted to a rather selfcontained introduction to group actions on complex and symplectic manifolds and to Borel-Weil theory in finite dimensions. These are followed by a treatment of the basics of infinite dimensional Lie groups, their actions and their representations. Finally, a number of more specialized and advanced topics are discussed, e.g., Borel-Weil theory for loop groups, aspects of the Virasoro algebra, (gauge) group actions and determinant bundles, and second quantization and the geometry of the infinite dimensional Grassmann manifold | ||
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Datensatz im Suchindex
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| dewey-ones | 510 - Mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-8227-9 |
| format | Electronic eBook |
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| id | DE-604.BV042422072 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034882279 9783764366025 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857489 |
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| physical | 1 Online-Ressource (XIII, 375p) |
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| publishDate | 2001 |
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| spelling | Huckleberry, Alan Verfasser aut Infinite Dimensional Kähler Manifolds edited by Alan Huckleberry, Tilmann Wurzbacher Basel Birkhäuser Basel 2001 1 Online-Ressource (XIII, 375p) txt rdacontent c rdamedia cr rdacarrier DMV Seminar Band 31 Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Having been used mainly as a tool for the study of finite dimensional objects, the emphasis has changed and they are now frequently studied for their own independent interest. On the one hand this is a collection of closely related articles on infinite dimensional Kähler manifolds and associated group actions which grew out of a DMV-Seminar on the same subject. On the other hand it covers significantly more ground than was possible during the seminar in Oberwolfach and is in a certain sense intended as a systematic approach which ranges from the foundations of the subject to recent developments. It should be accessible to doctoral students and as well researchers coming from a wide range of areas. The initial chapters are devoted to a rather selfcontained introduction to group actions on complex and symplectic manifolds and to Borel-Weil theory in finite dimensions. These are followed by a treatment of the basics of infinite dimensional Lie groups, their actions and their representations. Finally, a number of more specialized and advanced topics are discussed, e.g., Borel-Weil theory for loop groups, aspects of the Virasoro algebra, (gauge) group actions and determinant bundles, and second quantization and the geometry of the infinite dimensional Grassmann manifold Mathematics Mathematics, general Mathematik Kähler-Mannigfaltigkeit (DE-588)4162978-4 gnd rswk-swf Unendlichdimensionale Mannigfaltigkeit (DE-588)4433823-5 gnd rswk-swf Kähler-Mannigfaltigkeit (DE-588)4162978-4 s Unendlichdimensionale Mannigfaltigkeit (DE-588)4433823-5 s 1\p DE-604 Wurzbacher, Tilmann Sonstige oth https://doi.org/10.1007/978-3-0348-8227-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Huckleberry, Alan Infinite Dimensional Kähler Manifolds Mathematics Mathematics, general Mathematik Kähler-Mannigfaltigkeit (DE-588)4162978-4 gnd Unendlichdimensionale Mannigfaltigkeit (DE-588)4433823-5 gnd |
| subject_GND | (DE-588)4162978-4 (DE-588)4433823-5 |
| title | Infinite Dimensional Kähler Manifolds |
| title_auth | Infinite Dimensional Kähler Manifolds |
| title_exact_search | Infinite Dimensional Kähler Manifolds |
| title_full | Infinite Dimensional Kähler Manifolds edited by Alan Huckleberry, Tilmann Wurzbacher |
| title_fullStr | Infinite Dimensional Kähler Manifolds edited by Alan Huckleberry, Tilmann Wurzbacher |
| title_full_unstemmed | Infinite Dimensional Kähler Manifolds edited by Alan Huckleberry, Tilmann Wurzbacher |
| title_short | Infinite Dimensional Kähler Manifolds |
| title_sort | infinite dimensional kahler manifolds |
| topic | Mathematics Mathematics, general Mathematik Kähler-Mannigfaltigkeit (DE-588)4162978-4 gnd Unendlichdimensionale Mannigfaltigkeit (DE-588)4433823-5 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Kähler-Mannigfaltigkeit Unendlichdimensionale Mannigfaltigkeit |
| url | https://doi.org/10.1007/978-3-0348-8227-9 |
| work_keys_str_mv | AT huckleberryalan infinitedimensionalkahlermanifolds AT wurzbachertilmann infinitedimensionalkahlermanifolds |