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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Lattice (discrete subgroup) ： ウィキペディア英語版 Lattice (discrete subgroup) 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 R''n'', this amounts to the usual geometric notion of a lattice, 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. == Definition == Let ''G'' be a locally compact topological group with the Haar measure ''μ''. A discrete subgroup ''Γ'' is called a lattice in ''G'' if the quotient space ''G''/''Γ'' has finite invariant measure, that is, if ''G'' is a unimodular group and the volume ''μ''(''G''/''Γ'') is finite. The lattice is uniform (or ''cocompact'') if the quotient space is compact, and nonuniform otherwise. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lattice (discrete subgroup)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.