Geodesic
Semigroup Actions on Adjoint Orbits
Journal of Lie theory, Tome 22 (2012) no. 4, pp. 931-948
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Let $G$ be a connected semi-simple Lie group with finite center and $S\subset G$ a subsemigroup with ${\rm int}\, S\neq \emptyset$. In this article we study the control sets for the actions of $S$ on the adjoint orbits ${\rm Ad}(G)H$, where $H$ is a regular element in the Lie algebra of $G$. We show here that these sets can be described as sets of fixed points for regular elements in the interior of $S$. Moreover, we shall describe the domains of attraction of this control sets and show that these sets are not comparable with respect to the natural order on control sets.
Classification : 22F30
Mots-clés : Semigroup, adjoint orbits, regular elements 
@article{JLT_2012_22_4_JLT_2012_22_4_a1,
     author = {O. G. do Rocio and L. A. B. San Martin and M. A. Verdi},
     title = {Semigroup {Actions} on {Adjoint} {Orbits}},
     journal = {Journal of Lie theory},
     pages = {931--948},
     year = {2012},
     volume = {22},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2012_22_4_JLT_2012_22_4_a1/}
}
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O. G. do Rocio; L. A. B. San Martin; M. A. Verdi. Semigroup Actions on Adjoint Orbits. Journal of Lie theory, Tome 22 (2012) no. 4, pp. 931-948. http://geodesic.mathdoc.fr/item/JLT_2012_22_4_JLT_2012_22_4_a1/