Mathematics – Differential Geometry
Scientific paper
2010-03-31
Mathematics
Differential Geometry
v3 : version to be published in Journal of Geometry and Physics
Scientific paper
10.1016/j.geomphys.2011.11.002
In this paper we show how connections and their generalizations on transitive Lie algebroids are related to the notion of connections in the framework of the derivation-based noncommutative geometry. In order to compare the two constructions, we emphasize the algebraic approach of connections on Lie algebroids, using a suitable differential calculus. Two examples allow this comparison: on the one hand, the Atiyah Lie algebroid of a principal fiber bundle and, on the other hand, the space of derivations of the algebra of endomorphisms of a $SL(n, \mathbb{C})$-vector bundle. Gauge transformations are also considered in this comparison.
Lazzarini Serge
Masson Thierry
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