A Lie groupoid over is a groupoid for which and are differentiable manifolds and and multiplication are differentiable maps. Furthermore, the derivatives of and are required to have maximal matrix rank everywhere. Here, and are maps from onto .
Lie Groupoid
See also
Groupoid, Lie Algebroid, Nilpotent Lie Group, Semisimple Lie Group, Solvable Lie GroupExplore with Wolfram|Alpha
References
Weinstein, A. "Groupoids: Unifying Internal and External Symmetry." Not. Amer. Math. Soc. 43, 744-752, 1996.Referenced on Wolfram|Alpha
Lie GroupoidCite this as:
Weisstein, Eric W. "Lie Groupoid." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LieGroupoid.html