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Results tagged with lie-algebroids
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user 527050
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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First examples of Lie-Rinehart algebras that are not coming from Lie algebroids
Yes, there are many such Lie-Rinehart algebras. To understand such examples we need to recall some classical geometric results.
Note that a $C^\infty(M)$- module is the space of global sections of a s …
