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

Authors

  • Christoph Kawan Universitat Augsburg.
  • Osvaldo Germano do Rocio Universidade Estadual de Maringá.
  • Alexandre J. Santana Universidade Estadual de Maringá.

DOI:

https://doi.org/10.4067/S0716-09172011000200004

Keywords:

Topological conjugacy, Flows, Semi-simple Lie groups, Nilpotent Lie group, Affine groups.

Abstract

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

References

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[8] O. G. Rocio, A. J. Santana and M. A. Verdi, Semigroups of Affine Groups, Controllability of Affine Systems and Affine Bilinear Systems in Sl(2,)2, SIAM J. Control Optim. 48, pp. 1080—1088, (2009).

Published

2011-12-10

How to Cite

[1]
C. Kawan, O. G. do Rocio, and A. J. Santana, “On topological conjugacy of left invariant flows on semisimple and affine lie groups”, Proyecciones (Antofagasta, On line), vol. 30, no. 2, pp. 175-188, Dec. 2011.

Issue

Section

Artículos