On topological conjugacy of left invariant flows on semisimple and affine Lie groups

In this paper, we study the flows of nonzero left invariant vector fields on Lie groups with respect to topological conjugacy. Using the fundamental domain method, we are able to show that on a simply connected nilpotent Lie group any such flows are topologically conjugate. Combining this result wit...

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Autores principales:	Kawan,Christoph, Rocío,Osvaldo G, Santana,Alexandre J
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2011
Materias:	topological conjugacy flows semi-simple Lie groups nilpotent Lie group affine groups
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000200004
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spelling	oai:scielo:S0716-091720110002000042014-11-05On topological conjugacy of left invariant flows on semisimple and affine Lie groupsKawan,ChristophRocío,Osvaldo GSantana,Alexandre J topological conjugacy flows semi-simple Lie groups nilpotent Lie group affine groups In this paper, we study the flows of nonzero left invariant vector fields on Lie groups with respect to topological conjugacy. Using the fundamental domain method, we are able to show that on a simply connected nilpotent Lie group any such flows are topologically conjugate. Combining this result with the Iwasawa decomposition, we find that on a noncompact semisimple Lie group the flows of two nilpotent or abelian fields are topologically conjugate. Finally, for affine groups G = HV , V E" n, we show that the conjugacy class of a left invariant vector field does not depend on its Euclidean component.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.30 n.2 20112011-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000200004en10.4067/S0716-09172011000200004
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	topological conjugacy flows semi-simple Lie groups nilpotent Lie group affine groups
spellingShingle	topological conjugacy flows semi-simple Lie groups nilpotent Lie group affine groups Kawan,Christoph Rocío,Osvaldo G Santana,Alexandre J On topological conjugacy of left invariant flows on semisimple and affine Lie groups
description	In this paper, we study the flows of nonzero left invariant vector fields on Lie groups with respect to topological conjugacy. Using the fundamental domain method, we are able to show that on a simply connected nilpotent Lie group any such flows are topologically conjugate. Combining this result with the Iwasawa decomposition, we find that on a noncompact semisimple Lie group the flows of two nilpotent or abelian fields are topologically conjugate. Finally, for affine groups G = HV , V E" n, we show that the conjugacy class of a left invariant vector field does not depend on its Euclidean component.
author	Kawan,Christoph Rocío,Osvaldo G Santana,Alexandre J
author_facet	Kawan,Christoph Rocío,Osvaldo G Santana,Alexandre J
author_sort	Kawan,Christoph
title	On topological conjugacy of left invariant flows on semisimple and affine Lie groups
title_short	On topological conjugacy of left invariant flows on semisimple and affine Lie groups
title_full	On topological conjugacy of left invariant flows on semisimple and affine Lie groups
title_fullStr	On topological conjugacy of left invariant flows on semisimple and affine Lie groups
title_full_unstemmed	On topological conjugacy of left invariant flows on semisimple and affine Lie groups
title_sort	on topological conjugacy of left invariant flows on semisimple and affine lie groups
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2011
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000200004
work_keys_str_mv	AT kawanchristoph ontopologicalconjugacyofleftinvariantflowsonsemisimpleandaffineliegroups AT rocioosvaldog ontopologicalconjugacyofleftinvariantflowsonsemisimpleandaffineliegroups AT santanaalexandrej ontopologicalconjugacyofleftinvariantflowsonsemisimpleandaffineliegroups
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On topological conjugacy of left invariant flows on semisimple and affine Lie groups

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