Lie Algebroids over Differentiable Stacks

Abstract

We develop a theory of Lie algebroids over differentiable stacks that extends the standard theory of Lie algebroids over manifolds. In particular we show that Lie algebroids satisfy descent for submersions, define the category of Lie algebroids over a differentiable stack, construct a cohomology theory for these objects, and explain the relation to the theory of $\mathcal{L}\mathcal{A}$-groupoids. We construct a number of examples.

98 pages; PhD thesis

Cited by in corpus (5)

• Leaves of stacky Lie algebroids
• Flat vector bundles and analytic torsion on orbifolds
• On the Lie 2-algebra of sections of an LA-groupoid
• Poisson Structures on Moduli Spaces of Higgs Bundles over Stacky Curves
• Lie theory of vector bundles, Poisson geometry and double structures