Results 181 to 190 of about 2,887 (210)

DISCRETE SUBGROUPS OF REAL SEMISIMPLE LIE GROUPS

Mathematics of the USSR-Sbornik, 1969
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Discreteness of lattices of closed subgroups of lie groups

Ukrainian Mathematical Journal, 1986
Let G be a locally compact group and let L(G) be the set of all closed subgroups of G. The family \(\{\) \(F\in L(G) :\) \(H\subseteq F\subseteq HU\}\) forms the base of a topology \(\tau\) on L(G) (H\(\in L(G)\), U runs over a neighbourhood base of unit of G). It is proved that the space \(L_{\tau}(G)\) is discrete iff G is a Lie group.
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Profinite Groups and Discrete Subgroups of Lie Groups

2003
Workshop ...
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Discrete Subgroups of Lie Groups

1972
Résumé
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Pro-Lie groups approximable by discrete subgroups

Forum Mathematicum, 2014
Abstract A locally compact group G is said to be approximable by discrete subgroups if there exists a sequence of discrete subgroups (
Hatem Hamrouni, Bilel Kadri
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Discrete Subgroups Isomorphic to Lattices in Semisimple Lie Groups

American Journal of Mathematics, 1976
Let G be a locally compact topological group. A discrete subgroup T of G is said to be a lattice in G if the homogeneous space G/T carries a finite G invariant measure. A lattice T in G is said to be uniform if G/T is compact otherwise, it is said to be nonuniform.
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DISCRETE SUBGROUPS OF SOLVABLE LIE GROUPS OF TYPE $ (E)$

Mathematics of the USSR-Sbornik, 1971
Let and be simply connected Lie groups, and let be a lattice in . In the present article we investigate the question whether the homomorphism can be lifted to a homomorphism for the case that or is a Lie group of type . Incidentally we prove some of the properties of lattices in such groups.Bibliography: 13 items.
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Discrete Subgroups of Semisimple Lie Groups

1991
1. Statement of Main Results.- 2. Synopsis of the Chapters.- 3. Remarks on the Structure of the Book, References and Notation.- 1. Preliminaries.- 0. Notation, Terminology and Some Basic Facts.- 1. Algebraic Groups Over Arbitrary Fields.- 2. Algebraic Groups Over Local Fields.- 3. Arithmetic Groups.- 4. Measure Theory and Ergodic Theory.- 5.
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A note on discrete uniform subgroups of Lie groups

Geometriae Dedicata, 1986
Let G be an n-dimensional connected Lie group with a left invariant Riemannian metric \(\rho\) on G. Let \(\| \|\) denote the norm on the Lie algebra \({\mathfrak G}\) of G corresponding to \(\rho\) and let k(\(\rho)\) denote the norm of the Lie bracket i.e. \(k(\rho)=\max \{\| [X,Y]\|:\) X,Y\(\in {\mathfrak G}\), \(\| X\| \leq 1\), \(\| Y\| \leq 1\}\).
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Discrete Cocompact Subgroups of the Generic Filiform Nilpotent Lie Groups

Journal of Lie Theory, 2008
Let \({\mathcal L}_n\), \(n\geq 2\), be the filiform Lie algebra, namely \({\mathcal L}_n= \langle X_1,\dots, X_{n+1}\rangle_{\mathbb{R}}\) with non-trivial bracket relations \([X_{n+1}, X_j]= X_{j-1}\) \((2\leq j\leq n)\). Let \(L_n= \exp({\mathcal L}_n)\) be the associated connected and simply connected nilpotent Lie group.
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