Discrete Cocompact Subgroups of the Five-Dimensional Connected and Simply Connected Nilpotent Lie Groups

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...

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Main Authors: Amira Ghorbel, Hatem Hamrouni
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2009-02-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
nilpotent Lie group
discrete subgroup
nil-manifold
rational structures
Smith normal form
Hermite normal form
Online Access:http://dx.doi.org/10.3842/SIGMA.2009.020
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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
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