A topological conjugacy of invariant  flows on some class of Lie groups

Alexandre J. Santana; Simão N. Stelmastchuk

doi:10.5269/bspm.v38i3.37216

A topological conjugacy of invariant flows on some class of Lie groups

Alexandre J. Santana State University of Maringa Department of Mathematics
Simão N. Stelmastchuk Federal University of Parana Department of Mathematics http://orcid.org/0000-0002-4342-1230

DOI: https://doi.org/10.5269/bspm.v38i3.37216

Keywords: Topological conjugacy, Invariant flows, Lie groups

Abstract

The aim of this paper is to classify invariant flows on Lie group $G$ whose Lie algebra $\mathfrak{g}$ is associative or semisimple. Specifically, we present this classification from the hyperbolicity of the lift flows on $G \times \mathfrak{g}$. Then we apply this construction to some special cases as ${\rm Gl}(2,{\Bbb R})$ and affine Lie group.