Almost Lie Algebroids and Characteristic Classes

Abstract

Almost Lie algebroids are generalizations of Lie algebroids, when the Jacobiator is not necessary null. A simple example is given, for which a Lie algebroid bracket or a Courant bundle is not possible for the given anchor, but a natural extension of the bundle and the new anchor allows a Lie algebroid bracket. A cohomology and related characteristic classes of an almost Lie algebroid are also constructed. We prove that these characteristic classes are all pull-backs of the characteristic classes of the base space, as in the case of a Lie algebroid.

References in corpus (8)

• Brackets
• Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic Mechanics
• The Pontryagin Class for Pre-Courant Algebroids
• Pre-Courant Algebroids
• Poisson structures on almost complex Lie algebroids
• Cohomology for almost Lie algebroids
• Pontryagin Maximum Principle - a generalization
• Some results on the Mackenzie obstruction for transitive Lie algebroids

Cited by in corpus (4)

• 'Anti-Commutable' Pre-Leibniz Algebroids and Admissible Connections
• On the Bochner technique for singular distributions
• On longitudinal differential operators and Nash blowups
• Symmetric brackets induced by connections with totally skew-symmetric torsion on skew-symmetric algebroids