A lattice in a locally compact group 
is a discrete subgroup 
for which 
has a finite nonzero 
-invariant measure. This measure is obtained from
Haar measure and its total mass is the covolume.
A lattice is uniform when 
is compact. For example, 
is a uniform lattice, with a fundamental
domain of volume 1. The Euclidean lattice definition is a special case, while
lattices in noncommutative groups also occur in rigidity questions for twisted group
von Neumann algebras.
Lattice in a Locally Compact Group
See also
Haar Measure, Lattice, Locally Compact Group, Twisted Group von Neumann AlgebraExplore with Wolfram|Alpha
References
Gelander, T. "Lectures on Lattices and Locally Symmetric Spaces." 5 Feb 2014. https://arxiv.org/abs/1402.0962.Cite this as:
Weisstein, Eric W. "Lattice in a Locally Compact Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LatticeinaLocallyCompactGroup.html