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- Lattice_(discrete_subgroup) 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.".
- Lattice_(discrete_subgroup) thumbnail HeisenbergCayleyGraph.png?width=300.
- Lattice_(discrete_subgroup) wikiPageExternalLink IntroArithGroups.html.
- Lattice_(discrete_subgroup) wikiPageID "15782871".
- Lattice_(discrete_subgroup) wikiPageLength "7395".
- Lattice_(discrete_subgroup) wikiPageOutDegree "60".
- Lattice_(discrete_subgroup) wikiPageRevisionID "696329512".
- Lattice_(discrete_subgroup) wikiPageWikiLink Adele_ring.
- Lattice_(discrete_subgroup) wikiPageWikiLink Adelic_algebraic_group.
- Lattice_(discrete_subgroup) wikiPageWikiLink Alexander_Lubotzky.
- Lattice_(discrete_subgroup) wikiPageWikiLink Algebraic_number_theory.
- Lattice_(discrete_subgroup) wikiPageWikiLink Arithmetic_group.
- Lattice_(discrete_subgroup) wikiPageWikiLink Armand_Borel.
- Lattice_(discrete_subgroup) wikiPageWikiLink Automorphic_form.
- Lattice_(discrete_subgroup) wikiPageWikiLink Automorphism.
- Lattice_(discrete_subgroup) wikiPageWikiLink Category:Algebraic_groups.
- Lattice_(discrete_subgroup) wikiPageWikiLink Category:Ergodic_theory.
- Lattice_(discrete_subgroup) wikiPageWikiLink Category:Lie_groups.
- Lattice_(discrete_subgroup) wikiPageWikiLink Compact_space.
- Lattice_(discrete_subgroup) wikiPageWikiLink Discrete_group.
- Lattice_(discrete_subgroup) wikiPageWikiLink Ergebnisse_der_Mathematik_und_ihrer_Grenzgebiete.
- Lattice_(discrete_subgroup) wikiPageWikiLink George_Mostow.
- Lattice_(discrete_subgroup) wikiPageWikiLink Global_field.
- Lattice_(discrete_subgroup) wikiPageWikiLink Graph_of_groups.
- Lattice_(discrete_subgroup) wikiPageWikiLink Grigory_Margulis.
- Lattice_(discrete_subgroup) wikiPageWikiLink Haar_measure.
- Lattice_(discrete_subgroup) wikiPageWikiLink Harish-Chandra.
- Lattice_(discrete_subgroup) wikiPageWikiLink Hyman_Bass.
- Lattice_(discrete_subgroup) wikiPageWikiLink Integer.
- Lattice_(discrete_subgroup) wikiPageWikiLink Invariant_measure.
- Lattice_(discrete_subgroup) wikiPageWikiLink Jacques_Tits.
- Lattice_(discrete_subgroup) wikiPageWikiLink Kazhdans_property_(T).
- Lattice_(discrete_subgroup) wikiPageWikiLink Lattice_(group).
- Lattice_(discrete_subgroup) wikiPageWikiLink Lie_group.
- Lattice_(discrete_subgroup) wikiPageWikiLink Lie_theory.
- Lattice_(discrete_subgroup) wikiPageWikiLink Local_field.
- Lattice_(discrete_subgroup) wikiPageWikiLink Localization_of_a_ring.
- Lattice_(discrete_subgroup) wikiPageWikiLink Locally_compact_space.
- Lattice_(discrete_subgroup) wikiPageWikiLink M._S._Raghunathan.
- Lattice_(discrete_subgroup) wikiPageWikiLink Mathematics.
- Lattice_(discrete_subgroup) wikiPageWikiLink Modular_group.
- Lattice_(discrete_subgroup) wikiPageWikiLink Mostow_rigidity_theorem.
- Lattice_(discrete_subgroup) wikiPageWikiLink Nilpotent_group.
- Lattice_(discrete_subgroup) wikiPageWikiLink P-adic_number.
- Lattice_(discrete_subgroup) wikiPageWikiLink Quotient_space_(topology).
- Lattice_(discrete_subgroup) wikiPageWikiLink Robert_Zimmer.
- Lattice_(discrete_subgroup) wikiPageWikiLink SL2(R).
- Lattice_(discrete_subgroup) wikiPageWikiLink Semisimple_algebraic_group.
- Lattice_(discrete_subgroup) wikiPageWikiLink Special_linear_group.
- Lattice_(discrete_subgroup) wikiPageWikiLink Springer_Science+Business_Media.
- Lattice_(discrete_subgroup) wikiPageWikiLink Superrigidity.
- Lattice_(discrete_subgroup) wikiPageWikiLink Topological_group.
- Lattice_(discrete_subgroup) wikiPageWikiLink Tree_(graph_theory).
- Lattice_(discrete_subgroup) wikiPageWikiLink Tsuneo_Tamagawa.
- Lattice_(discrete_subgroup) wikiPageWikiLink File:HeisenbergCayleyGraph.png.
- Lattice_(discrete_subgroup) wikiPageWikiLinkText "Lattice (discrete subgroup)".
- Lattice_(discrete_subgroup) wikiPageWikiLinkText "lattice".
- Lattice_(discrete_subgroup) wikiPageWikiLinkText "lattices".
- Lattice_(discrete_subgroup) wikiPageWikiLinkText "sublattice".
- Lattice_(discrete_subgroup) wikiPageWikiLinkText "uniform subgroup".
- Lattice_(discrete_subgroup) wikiPageUsesTemplate Template:Citation.
- Lattice_(discrete_subgroup) wikiPageUsesTemplate Template:Group_theory_sidebar.
- Lattice_(discrete_subgroup) wikiPageUsesTemplate Template:MR.
- Lattice_(discrete_subgroup) subject Category:Algebraic_groups.
- Lattice_(discrete_subgroup) subject Category:Ergodic_theory.
- Lattice_(discrete_subgroup) subject Category:Lie_groups.
- Lattice_(discrete_subgroup) hypernym Subgroup.
- Lattice_(discrete_subgroup) type EthnicGroup.
- Lattice_(discrete_subgroup) type Group.
- Lattice_(discrete_subgroup) type Group.
- Lattice_(discrete_subgroup) type Process.
- Lattice_(discrete_subgroup) type Variety.
- Lattice_(discrete_subgroup) 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.".
- Lattice_(discrete_subgroup) label "Lattice (discrete subgroup)".
- Lattice_(discrete_subgroup) sameAs Q6497088.
- Lattice_(discrete_subgroup) sameAs 局所コンパクト群における格子.
- Lattice_(discrete_subgroup) sameAs m.03ntfnr.
- Lattice_(discrete_subgroup) sameAs Q6497088.
- Lattice_(discrete_subgroup) wasDerivedFrom Lattice_(discrete_subgroup)?oldid=696329512.
- Lattice_(discrete_subgroup) depiction HeisenbergCayleyGraph.png.
- Lattice_(discrete_subgroup) isPrimaryTopicOf Lattice_(discrete_subgroup).