Extensions of Lie Brackets

Details Extensions of Lie Brackets Extensions of Lie Brackets

2008-10-08

arxiv.org/abs/0810.1462v5

Mathematics

Differential Geometry

34 pages

Scientific paper

We provide a framework for extensions of Lie algebroids, including non-abelian extensions and Lie algebroids over different bases. Our approach involves Ehresmann connections, which allows straight generalizations of classical constructions. We exhibit a filtration in cohomology and explain the associated spectral sequence. We also give a description of the groupoid integrating an extension in case a complete connection can be fixed. The problem of integrability is also studied.

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