Namespaces
Variants
Actions

Lattice in a Lie group

From Encyclopedia of Mathematics
Jump to: navigation, search

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.

How to Cite This Entry:
Lattice in a Lie group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lattice_in_a_Lie_group&oldid=53775
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

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners in accordance with our Privacy Policy. You can manage your preferences in 'Manage Cookies'.