Lie groupoids and Lie algebroids in differential geometry:
This book provides a striking synthesis of the standard theory of connections in principal bundles and the Lie theory of Lie groupoids. The concept of Lie groupoid is a little-known formulation of the concept of principal bundle and corresponding to the Lie algebra of a Lie group is the concept of L...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
1987
|
| Series: | London Mathematical Society lecture note series
124 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | This book provides a striking synthesis of the standard theory of connections in principal bundles and the Lie theory of Lie groupoids. The concept of Lie groupoid is a little-known formulation of the concept of principal bundle and corresponding to the Lie algebra of a Lie group is the concept of Lie algebroid: in principal bundle terms this is the Atiyah sequence. The author's viewpoint is that certain deep problems in connection theory are best addressed by groupoid and Lie algebroid methods. After preliminary chapters on topological groupoids, the author gives the first unified and detailed account of the theory of Lie groupoids and Lie algebroids. He then applies this theory to the cohomology of Lie algebroids, re-interpreting connection theory in cohomological terms, and giving criteria for the existence of (not necessarily Riemannian) connections with prescribed curvature form. This material, presented in the last two chapters, is work of the author published here for the first time. This book will be of interest to differential geometers working in general connection theory and to researchers in theoretical physics and other fields who make use of connection theory |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xvi, 327 pages) |
| ISBN: | 9780511661839 |
| DOI: | 10.1017/CBO9780511661839 |
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| 520 | |a This book provides a striking synthesis of the standard theory of connections in principal bundles and the Lie theory of Lie groupoids. The concept of Lie groupoid is a little-known formulation of the concept of principal bundle and corresponding to the Lie algebra of a Lie group is the concept of Lie algebroid: in principal bundle terms this is the Atiyah sequence. The author's viewpoint is that certain deep problems in connection theory are best addressed by groupoid and Lie algebroid methods. After preliminary chapters on topological groupoids, the author gives the first unified and detailed account of the theory of Lie groupoids and Lie algebroids. He then applies this theory to the cohomology of Lie algebroids, re-interpreting connection theory in cohomological terms, and giving criteria for the existence of (not necessarily Riemannian) connections with prescribed curvature form. This material, presented in the last two chapters, is work of the author published here for the first time. This book will be of interest to differential geometers working in general connection theory and to researchers in theoretical physics and other fields who make use of connection theory | ||
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Record in the Search Index
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|---|---|
| any_adam_object | |
| author | Mackenzie, K. |
| author_facet | Mackenzie, K. |
| author_role | aut |
| author_sort | Mackenzie, K. |
| author_variant | k m km |
| building | Verbundindex |
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| dewey-full | 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/6 |
| dewey-search | 516.3/6 |
| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| format | Electronic eBook |
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| id | DE-604.BV043942152 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:17Z |
| institution | BVB |
| isbn | 9780511661839 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351122 |
| oclc_num | 967601664 |
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| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xvi, 327 pages) |
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| publishDate | 1987 |
| publishDateSearch | 1987 |
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| publisher | Cambridge University Press |
| record_format | marc |
| series2 | London Mathematical Society lecture note series |
| spelling | Mackenzie, K. Verfasser aut Lie groupoids and Lie algebroids in differential geometry K. Mackenzie Lie Groupoids & Lie Algebroids in Differential Geometry Cambridge Cambridge University Press 1987 1 online resource (xvi, 327 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 124 Title from publisher's bibliographic system (viewed on 05 Oct 2015) This book provides a striking synthesis of the standard theory of connections in principal bundles and the Lie theory of Lie groupoids. The concept of Lie groupoid is a little-known formulation of the concept of principal bundle and corresponding to the Lie algebra of a Lie group is the concept of Lie algebroid: in principal bundle terms this is the Atiyah sequence. The author's viewpoint is that certain deep problems in connection theory are best addressed by groupoid and Lie algebroid methods. After preliminary chapters on topological groupoids, the author gives the first unified and detailed account of the theory of Lie groupoids and Lie algebroids. He then applies this theory to the cohomology of Lie algebroids, re-interpreting connection theory in cohomological terms, and giving criteria for the existence of (not necessarily Riemannian) connections with prescribed curvature form. This material, presented in the last two chapters, is work of the author published here for the first time. This book will be of interest to differential geometers working in general connection theory and to researchers in theoretical physics and other fields who make use of connection theory Connections (Mathematics) Lie groupoids Lie algebroids Fiber bundles (Mathematics) Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Lie-Gruppoid (DE-588)4224180-7 gnd rswk-swf Gruppoid (DE-588)4158484-3 gnd rswk-swf Lie-Algebroid (DE-588)4630863-5 gnd rswk-swf Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Algebroid (DE-588)4630863-5 s Differentialgeometrie (DE-588)4012248-7 s 1\p DE-604 Lie-Gruppoid (DE-588)4224180-7 s 2\p DE-604 Gruppoid (DE-588)4158484-3 s Lie-Algebra (DE-588)4130355-6 s 3\p DE-604 Erscheint auch als Druckausgabe 978-0-521-34882-9 https://doi.org/10.1017/CBO9780511661839 Verlag URL des Erstveröffentlichers 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 | Mackenzie, K. Lie groupoids and Lie algebroids in differential geometry Connections (Mathematics) Lie groupoids Lie algebroids Fiber bundles (Mathematics) Differentialgeometrie (DE-588)4012248-7 gnd Lie-Gruppoid (DE-588)4224180-7 gnd Gruppoid (DE-588)4158484-3 gnd Lie-Algebroid (DE-588)4630863-5 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4224180-7 (DE-588)4158484-3 (DE-588)4630863-5 (DE-588)4130355-6 |
| title | Lie groupoids and Lie algebroids in differential geometry |
| title_alt | Lie Groupoids & Lie Algebroids in Differential Geometry |
| title_auth | Lie groupoids and Lie algebroids in differential geometry |
| title_exact_search | Lie groupoids and Lie algebroids in differential geometry |
| title_full | Lie groupoids and Lie algebroids in differential geometry K. Mackenzie |
| title_fullStr | Lie groupoids and Lie algebroids in differential geometry K. Mackenzie |
| title_full_unstemmed | Lie groupoids and Lie algebroids in differential geometry K. Mackenzie |
| title_short | Lie groupoids and Lie algebroids in differential geometry |
| title_sort | lie groupoids and lie algebroids in differential geometry |
| topic | Connections (Mathematics) Lie groupoids Lie algebroids Fiber bundles (Mathematics) Differentialgeometrie (DE-588)4012248-7 gnd Lie-Gruppoid (DE-588)4224180-7 gnd Gruppoid (DE-588)4158484-3 gnd Lie-Algebroid (DE-588)4630863-5 gnd Lie-Algebra (DE-588)4130355-6 gnd |
| topic_facet | Connections (Mathematics) Lie groupoids Lie algebroids Fiber bundles (Mathematics) Differentialgeometrie Lie-Gruppoid Gruppoid Lie-Algebroid Lie-Algebra |
| url | https://doi.org/10.1017/CBO9780511661839 |
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