Lie Algebroid

The infinitesimal algebraic object associated with a Lie Groupoid. A Lie algebroid over a Manifold $B$ is a Vector Bundle $A$ over $B$ with a Lie Algebra structure $[\,,\,]$ (Lie Bracket) on its Space of smooth sections together with its Anchor $\rho$.

See also Lie Algebra

References

Weinstein, A. ``Groupoids: Unifying Internal and External Symmetry.'' Not. Amer. Math. Soc. 43, 744-752, 1996.