Higher Extensions of Lie Algebroids

Understand

We study the extension of a Lie algebroid by a representation up to homotopy, including semidirect products of a Lie algebroid with such representations.

• The extension results in a higher Lie algebroid.
• We give exact Courant algebroids and string Lie 2-algebras as examples of such extensions.
• We then apply this to obtain a Lie 2-groupoid integration of an exact Courant algebroid.