Titlebook: Cartan Geometries and their Symmetries; A Lie Algebroid Appr Mike Crampin,David Saunders Book 2016 Atlantis Press and the author(s) 2016 Ca

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Connections on Lie Groupoids and Lie Algebroids,In this chapter we shall describe several different notions of connection. As well as introducing connections on Lie groupoids (path connections) and on Lie algebroids (infinitesimal connections) we shall see how these ideas are related to the classical concepts of covariant derivatives and, more generally, connections on vector bundles.

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Symmetries,re both finite and infinitesimal symmetries may be considered, the former being diffeomorphisms with a property such as preserving geodesics, horizontal lifts or something similar, and the latter being vector fields whose flows have the same property.

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