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 Resource. https://mathworld.wolfram.com/LieGroupoid.html