Lattice in a Lie group
A discrete subgroup \Gamma of a Lie group G such that G/\Gamma has a finite volume relative to the (induced) G-invariant measure.
A lattice of dimension n (or rank n) in a vector space V over \mathbf R or \mathbf C is a free Abelian subgroup in V generated by n linearly independent vectors over \mathbf R. A subgroup of the additive group of a finite-dimensional vector space V over \mathbf R is discrete if and only if it is a lattice [1].
References
[1] | S.A. Morris, "Pontryagin duality and the structure of locally compact Abelian groups" , London Math. Soc. Lecture Notes , 29 , Cambridge Univ. Press (1977) |
Comments
See also Discrete group of transformations.
Lattice in a Lie group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lattice_in_a_Lie_group&oldid=53775