Lattice in a Lie group

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A discrete subgroup of a Lie group such that has a finite volume relative to the (induced) -invariant measure.

A lattice of dimension (or rank) in a vector space over or is a free Abelian subgroup in generated by linearly independent vectors over . A subgroup of the additive group of a finite-dimensional vector space over is discrete if and only if it is a lattice [1].


[1] S.A. Morris, "Pontryagin duality and the structure of locally compact Abelian groups" , London Math. Soc. Lecture Notes , 29 , Cambridge Univ. Press (1977)


See also Discrete group of transformations.

How to Cite This Entry:
Lattice in a Lie group. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by r group','../u/u095350.htm','Unitary transformation','../u/u095590.htm','Vector bundle, analytic','../v/v096400.htm')" style="background-color:yellow;">A.L. Onishchik (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article