Extensions of Lie Brackets

Understand

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.