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arXiv · 1003.6106

Connections on Lie algebroids and on derivation-based noncommutative geometry

Serge Lazzarini·Thierry Masson
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Abstract

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.

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Serge Lazzarini, Thierry Masson. 2010-03-31. Connections on Lie algebroids and on derivation-based noncommutative geometry. https://doi.org/10.1016/j.geomphys.2011.11.002

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