%0 Journal Article
%T Connections on Lie algebroids and on derivation-based noncommutative geometry
%A Serge Lazzarini
%A Thierry Masson
%J Mathematics
%D 2010
%I arXiv
%R 10.1016/j.geomphys.2011.11.002
%X 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.
%U http://arxiv.org/abs/1003.6106v3