(1) Departamento de Matemática, Universidade Estadual de Maringá, Cx. Postal 331, 87.020-900, Maringá-Pr, Brasil and Departamento de Matemática, Imecc Universidade Estadual de Campinas, Cx. Postal 6065, 13.083-859 Campinas – SP, Brasil
Abstract:
This paper studies connected components of open subsemigroups of non-compact
semi-simple Lie groups by using control sets in the flag manifolds and their
coverings.
The concept of recurrent component is introduced and a method is given by
which their number can be computed. It is shown that the union of all
recurrent components is a semigroup. The idea of mid-reversibility comes up
to show that an open semigroup has just one semigroup component if the
identity belongs to its closure. A necessary and sufficient condition for
mid-reversibility is proved showing that e.g. in a complex group any open
semigroup is mid-reversible.