# Questions tagged [lie-algebroids]

In differential geometry, Lie algebroids generalize on one hand Lie algebras, on the other hand the tangent bundle of a manifold: they are vector bundles equipped with an anchor map, i.e. a vector bundle morphism to the tangent bundle, and a Lie algebra structure on the space of sections subject to certain Leibniz rules. The integrated version of a Lie algebroid is a Lie groupoid. A purely algebraic version is a Lie-Rinehart algebra.

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### Special cases of Lie II for groupoids using elementary techniques

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### Fibration on the category of Lie pseudoalgebras implementing comorphisms

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### Natural appeareances of (commutative) algebras in $\mathfrak g$-modules

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### Recovering the Weinstein Splitting Theorem for Poisson manifolds using the Local Splitting theorem for Lie algebroids

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### Generalisation of the notion of operad

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### Example of tensor category with non-simple unit $J\to \mathbb{1} \to Q$ and suitably extension $Q\to M\to J$

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### The connection between Lie algebroids and foliations

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### Is there a precisely formulable obstruction for the tangent bundle being a Lie algebra bundle?

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### Computation with Lie algebroid differential?

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### Lie Groupoid of a Transitive Lie algebroid

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### Is $\mathbb{P}^1$ the only smooth projective curve with a locally split tangent lie algebroid?

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### Is every singular foliation induced by a Lie algebroid?

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### Lie Algebroid Structure on $A_M\times I\longrightarrow M\times I$?

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### Analogue of Kontsevich's formality theorem for quantization of Courant algebroids

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### Action of a Lie groupoid on a Lie Algebroid?

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### Property of Lie Algebroid Morphism?

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### Poisson structure on the dual Lie algebroid

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### Property of Lie algebroid morphism: $\#_B\circ \Phi=d\phi\circ \#_A$?

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### A-Paths as morphisms of Lie Algebroids $TI\longrightarrow A$?

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### Differentiation of Lie $\infty$-groupoids

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### Almost but not quite a Lie algebroid: what is it?

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### AKSZ sigma models for higher spin

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### Continuous and smooth Lie groupoid cohomology

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### What's an example of a commutative algebra over $\mathbb Q$ that fails to satisfy this version of the “PBW theorem”

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### For which algebras does \{Differential Operators\} satisfy a PBW-like theorem?

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### Differential forms on an almost complex manifold

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### Examples of Lie Algebroids

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### Is there any relation between deformation and extension of Lie algebras?

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### Geometry and Integrability in Other Bundles

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### Is the cohomology of the corresponding Lie algebroid an invariant under equivalence of source-simply-connected Lie groupoids?

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### When does a VBLA induce an isomorphism on Lie algebroid cohomology?

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### Do Lie algebroids pull back (along submersions)?

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