View source for Lattice in a Lie group

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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 [[#References|[1]]].

====References====
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<TR><TD valign="top">[1]</TD> <TD valign="top">  S.A. Morris,   "Pontryagin duality and the structure of locally compact Abelian groups" , ''London Math. Soc. Lecture Notes'' , '''29''' , Cambridge Univ. Press  (1977)</TD></TR>
</table>



====Comments====
See also [[Discrete group of transformations|Discrete group of transformations]].