Control sets on orbits and ordered compactification of semigroups / Conjuntos de controle em orbitas adjuntas e compactificações ordenadas de semigrupos
AUTOR(ES)
Marcos Andre Verdi
DATA DE PUBLICAÇÃO
2007
RESUMO
In this work we study two distinct problems: semigroup actions on adjoint orbits and compacti?cation of semigroups. For the study of the semigroup actions, we consider a semi-simple connected noncompact Lie group G and the adjoint orbit through elements in a maximal abelian subalgebra contained in the complement of a maximal compactly embedded subalgebra of the Lie algebra of G. We take then a semigroup S Ì G with interior points and describe the control sets for the S-action on these orbits. It is proved here that these control sets are no comparable and we describe its domains of attraction. We also consider the case in that S is a maximal semigroup and obtain a better description of the control sets. For the compacti?cation of semigroups, we use the same hypothesis about G and consider S as the compression semigroup of a closed subset in the maximal ?ag manifold of G. We obtain a compacti?cation of the homogeneous space G/H, where H=S ÇS-1, as a subset of the set of closed sets of G and we show that when G has rank one is possible to realize the image of S/H under this compacti?cation in the set of the closed subsets of the maximal ?ag manifold
ASSUNTO(S)
homogeneous spaces espaços homogeneos semigrupos lie groupos de semigroups lie groups
