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

• Kawan, Christoph ^[1] ; Rocio, Osvaldo Germano do ^[2] ; Santana, Alexandre J. ^[2]
  1. [1] University of Augsburg

     University of Augsburg

     Kreisfreie Stadt Augsburg, Alemania

     
  2. [2] Universidade Estadual de Maringá

     Universidade Estadual de Maringá

     Brasil

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 30, Nº. 2, 2011, págs. 175-188
• Idioma: inglés
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• Resumen

  • 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 ∼R n, we show that the conjugacy class of a left invariant vector field does not depend on its Euclidean component.