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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,...

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Detalles Bibliográficos
Autores principales: Crampin, Mike, Saunders, David
Lenguaje:eng
Publicado: Springer 2016
Materias:
Acceso en línea:https://dx.doi.org/10.2991/978-94-6239-192-5
http://cds.cern.ch/record/2157807
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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.
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institution Organización Europea para la Investigación Nuclear
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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