Journal of Lie Theory 22 (2012), No. 4, 931--948
Copyright Heldermann Verlag 2012
Semigroup Actions on Adjoint Orbits
Osvaldo G. do Rocio
Dep. de Matemática, Universidade Estadual de Maringá, UEM, Avenida Colombo 5790, 87020-900 - Maringá - PR, Brazil
rocio@uem.br
Luiz A. B. San Martin
Dep. de Matemática, Universidade Estadual de Campinas, UNICAMP, Cx. Postal 6065, 13.083-859 - Campinas - SP, Brazil
smartin@ime.unicamp.br
Marcos André Verdi
Dep. de Matemática, Universidade Estadual de Maringá, UEM, Avenida Colombo 5790, 87020-900 - Maringá - PR, Brazil
maverdi@uem.br
[Abstract-pdf]
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.
Keywords: Semigroup, adjoint orbits, regular elements.
MSC: 22F30
[ Fulltext-pdf (314 KB)] for subscribers only.