Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 15 (2019), 021, 12 pages      arXiv:1808.03116

Almost Lie Algebroids and Characteristic Classes

Marcela Popescu and Paul Popescu
University of Craiova, Faculty of Sciences, Department of Applied Mathematics, 13, ''Al. I. Cuza'' st., 200585 Craiova, Romania

Received August 10, 2018, in final form March 04, 2019; Published online March 20, 2019

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.

Key words: almost Lie algebroid; Jacobiator; characteristic classes.

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