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Hot answers tagged lie-algebroids

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

José, after your last comment, I am pretty sure that you are simply in the presence of a Jacobi structure on a nontrivial line bundle. Most of what I write below is taken from this paper by Crainic ...
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Is every singular foliation induced by a Lie algebroid?

It is possible to define the Lie groupoid of a singular foliation and associates to it its Lie algebroid when it is smooth. This Lie algebroid satisfies the property 2. https://projecteuclid.org/...
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Is every singular foliation induced by a Lie algebroid?

For Stefan-Sussmann singular foliations, the answer is negative: See Prop. 1.3 in the following paper, for the construction of an explicit counterexample: http://users.uoa.gr/~iandroul/...
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Accepted

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

If $f: X \to \mathbb A^n$ is an etale map, then we can pull back vector fields on $\mathbb A^n$ to vector fields on $X$. This pullback operation is a lie algebroid homomorphism. Hence if we pull back ...
• 122k

Connection between Grothendieck's homotopy hypothesis and Lie's second and third theorems?

There are analogues of Lie's theorems in homotopy theory, primarily for rational and $p$-adic homotopy types, as well as Lie ∞-groupoids, which can be seen as smooth homotopy types. In the rational ...
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Use of theory of Lie algebroids in (better) understanding of generalised complex structures

The compatibility conditions that you mention in the definition of a generalized complex structure are equivalent to the statement that the $+i$-eigenbundle $L$ of $J$ is a complex Dirac structure: ...
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references to learn the general theory Lie $\infty$-groupoids and Lie $\infty$-algebroids

There is no introductory book on Lie ∞-groupoids and ∞-algebroids analogous to Mackenzie's book. The only book-length treatment that covers these subjects is Urs Schreiber's Differential cohomology in ...
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Lie algebroid in algebraic geometry

I suggest having a look at Beĭlinson, A.; Bernstein, J. A proof of Jantzen conjectures. MR: Matches for: MR=1237825 §1.2 . https://people.math.harvard.edu/~gaitsgde/grad_2009/BB%20-%20Jantzen.pdf
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