Lattice in a Lie group
From Encyclopedia of Mathematics
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].
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=11363
Lattice in a Lie group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Lattice_in_a_Lie_group&oldid=11363
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