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Cartan geometries and their symmetries: a Lie algebroid approach
In this book we first review the ideas of Lie groupoid and Lie algebroid, and the associated concepts of connection. We next consider Lie groupoids of fibre morphisms of a fibre bundle, and the connections on such groupoids together with their symmetries. We also see how the infinitesimal approach,...
Autores principales: | , |
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Lenguaje: | eng |
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Springer
2016
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Materias: | |
Acceso en línea: | https://dx.doi.org/10.2991/978-94-6239-192-5 http://cds.cern.ch/record/2157807 |
_version_ | 1780950746189004800 |
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author | Crampin, Mike Saunders, David |
author_facet | Crampin, Mike Saunders, David |
author_sort | Crampin, Mike |
collection | CERN |
description | In this book we first review the ideas of Lie groupoid and Lie algebroid, and the associated concepts of connection. We next consider Lie groupoids of fibre morphisms of a fibre bundle, and the connections on such groupoids together with their symmetries. We also see how the infinitesimal approach, using Lie algebroids rather than Lie groupoids, and in particular using Lie algebroids of vector fields along the projection of the fibre bundle, may be of benefit. We then introduce Cartan geometries, together with a number of tools we shall use to study them. We take, as particular examples, the four classical types of geometry: affine, projective, Riemannian and conformal geometry. We also see how our approach can start to fit into a more general theory. Finally, we specialize to the geometries (affine and projective) associated with path spaces and geodesics, and consider their symmetries and other properties. |
id | cern-2157807 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2016 |
publisher | Springer |
record_format | invenio |
spelling | cern-21578072021-04-21T19:40:39Zdoi:10.2991/978-94-6239-192-5http://cds.cern.ch/record/2157807engCrampin, MikeSaunders, DavidCartan geometries and their symmetries: a Lie algebroid approachMathematical Physics and MathematicsIn this book we first review the ideas of Lie groupoid and Lie algebroid, and the associated concepts of connection. We next consider Lie groupoids of fibre morphisms of a fibre bundle, and the connections on such groupoids together with their symmetries. We also see how the infinitesimal approach, using Lie algebroids rather than Lie groupoids, and in particular using Lie algebroids of vector fields along the projection of the fibre bundle, may be of benefit. We then introduce Cartan geometries, together with a number of tools we shall use to study them. We take, as particular examples, the four classical types of geometry: affine, projective, Riemannian and conformal geometry. We also see how our approach can start to fit into a more general theory. Finally, we specialize to the geometries (affine and projective) associated with path spaces and geodesics, and consider their symmetries and other properties.Springeroai:cds.cern.ch:21578072016 |
spellingShingle | Mathematical Physics and Mathematics Crampin, Mike Saunders, David Cartan geometries and their symmetries: a Lie algebroid approach |
title | Cartan geometries and their symmetries: a Lie algebroid approach |
title_full | Cartan geometries and their symmetries: a Lie algebroid approach |
title_fullStr | Cartan geometries and their symmetries: a Lie algebroid approach |
title_full_unstemmed | Cartan geometries and their symmetries: a Lie algebroid approach |
title_short | Cartan geometries and their symmetries: a Lie algebroid approach |
title_sort | cartan geometries and their symmetries: a lie algebroid approach |
topic | Mathematical Physics and Mathematics |
url | https://dx.doi.org/10.2991/978-94-6239-192-5 http://cds.cern.ch/record/2157807 |
work_keys_str_mv | AT crampinmike cartangeometriesandtheirsymmetriesaliealgebroidapproach AT saundersdavid cartangeometriesandtheirsymmetriesaliealgebroidapproach |