Connections on Lie algebroids and on derivation-based noncommutative geometry

Details Connections on Lie algebroids and on derivation-based noncommutative geometry Connections on Lie algebroids and on derivation-based noncommutative geometry

2010-03-31

arxiv.org/abs/1003.6106v3

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.

Affiliated with

Also associated with

No associations

Rating

Connections on Lie algebroids and on derivation-based noncommutative geometry does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Connections on Lie algebroids and on derivation-based noncommutative geometry, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Connections on Lie algebroids and on derivation-based noncommutative geometry will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-580972