Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie Groups
The discrete cocompact subgroups of the five-dimensional connected, simply connected nilpotent Lie groups are determined up to isomorphism. Moreover, we prove if G = N × A is a connected, simply connected, nilpotent Lie group with an Abelian factor A, then every uniform subgroup of G is the direct p...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
National Academy of Science of Ukraine
2009-02-01
|
Series: | Symmetry, Integrability and Geometry: Methods and Applications |
Subjects: | |
Online Access: | http://dx.doi.org/10.3842/SIGMA.2009.020 |
id |
doaj-2e4d6e26da0e4556b8f7a47296a4d3f1 |
---|---|
record_format |
Article |
spelling |
doaj-2e4d6e26da0e4556b8f7a47296a4d3f12020-11-24T23:30:42ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592009-02-015020Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie GroupsAmira GhorbelHatem HamrouniThe discrete cocompact subgroups of the five-dimensional connected, simply connected nilpotent Lie groups are determined up to isomorphism. Moreover, we prove if G = N × A is a connected, simply connected, nilpotent Lie group with an Abelian factor A, then every uniform subgroup of G is the direct product of a uniform subgroup of N and Z^r where r = dim A.http://dx.doi.org/10.3842/SIGMA.2009.020nilpotent Lie groupdiscrete subgroupnil-manifoldrational structuresSmith normal formHermite normal form |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Amira Ghorbel Hatem Hamrouni |
spellingShingle |
Amira Ghorbel Hatem Hamrouni Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie Groups Symmetry, Integrability and Geometry: Methods and Applications nilpotent Lie group discrete subgroup nil-manifold rational structures Smith normal form Hermite normal form |
author_facet |
Amira Ghorbel Hatem Hamrouni |
author_sort |
Amira Ghorbel |
title |
Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie Groups |
title_short |
Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie Groups |
title_full |
Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie Groups |
title_fullStr |
Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie Groups |
title_full_unstemmed |
Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie Groups |
title_sort |
discrete cocompact subgroups of the five-dimensional connected and simply connected nilpotent lie groups |
publisher |
National Academy of Science of Ukraine |
series |
Symmetry, Integrability and Geometry: Methods and Applications |
issn |
1815-0659 |
publishDate |
2009-02-01 |
description |
The discrete cocompact subgroups of the five-dimensional connected, simply connected nilpotent Lie groups are determined up to isomorphism. Moreover, we prove if G = N × A is a connected, simply connected, nilpotent Lie group with an Abelian factor A, then every uniform subgroup of G is the direct product of a uniform subgroup of N and Z^r where r = dim A. |
topic |
nilpotent Lie group discrete subgroup nil-manifold rational structures Smith normal form Hermite normal form |
url |
http://dx.doi.org/10.3842/SIGMA.2009.020 |
work_keys_str_mv |
AT amiraghorbel discretecocompactsubgroupsofthefivedimensionalconnectedandsimplyconnectednilpotentliegroups AT hatemhamrouni discretecocompactsubgroupsofthefivedimensionalconnectedandsimplyconnectednilpotentliegroups |
_version_ |
1725540729913081856 |