Lie Groupoid

A Groupoid $G$ over $B$ for which $G$ and $B$ are differentiable manifolds and $\alpha$, $\beta$, and multiplication are differentiable maps. Furthermore, the derivatives of $\alpha$ and $\beta$ are required to have maximal Rank everywhere. Here, $\alpha$ and $\beta$ are maps from $G$ onto $\Bbb{R}^2$ with $\alpha:(x,\gamma,y)\mapsto x$ and $\beta:(x,\gamma,y)\mapsto y.$

See also Lie Algebroid, Nilpotent Lie Group, Semisimple Lie Group, Solvable Lie Group

References

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