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- Q6497088 subject Q7452174.
- Q6497088 subject Q7585268.
- Q6497088 subject Q8805755.
- Q6497088 abstract "In Lie theory and related areas of mathematics, a lattice in a locally compact topological group is a discrete subgroup with the property that the quotient space has finite invariant measure. In the special case of subgroups of Rn, this amounts to the usual geometric notion of a lattice (see the article Lattice (group)), and both the algebraic structure of lattices and the geometry of the totality of all lattices are relatively well understood. Deep results of Borel, Harish-Chandra, Mostow, Tamagawa, M. S. Raghunathan, Margulis, Zimmer obtained from the 1950s through the 1970s provided examples and generalized much of the theory to the setting of nilpotent Lie groups and semisimple algebraic groups over a local field. In the 1990s, Bass and Lubotzky initiated the study of tree lattices, which remains an active research area.".
- Q6497088 thumbnail HeisenbergCayleyGraph.png?width=300.
- Q6497088 wikiPageExternalLink IntroArithGroups.html.
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- Q6497088 wikiPageWikiLink Q7452174.
- Q6497088 wikiPageWikiLink Q7585268.
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- Q6497088 comment "In Lie theory and related areas of mathematics, a lattice in a locally compact topological group is a discrete subgroup with the property that the quotient space has finite invariant measure. In the special case of subgroups of Rn, this amounts to the usual geometric notion of a lattice (see the article Lattice (group)), and both the algebraic structure of lattices and the geometry of the totality of all lattices are relatively well understood.".
- Q6497088 label "Lattice (discrete subgroup)".
- Q6497088 depiction HeisenbergCayleyGraph.png.