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Results tagged with lie-algebroids
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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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Examples of Lie Algebroids
This is not particularly an answer to your question. Beyond Lie algebroids arising from Poisson structures (which Dima Shlyakhtenko has already mentioned in the comments), I think the Wikipedia list …
- 54.6k
0
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Is the cohomology of the corresponding Lie algebroid an invariant under equivalence of sourc...
Here is a counterexample to the second question. Let $\mathfrak g$ be the nonabelian two-dimensional Lie algebra, thought of as an algebroid with one object, and $G$ its simply-connected group, thoug …
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Is there any relation between deformation and extension of Lie algebras?
There are big pictures that I'll let others describe. Here's a little picture which cogeneralizes the Weinstein remark. (To "cogeneralize" is to make more specific, rather than less.)
Recall that a …
- 54.6k