Semigroups and control in semi-simple grups over local fields / Semigrupos e controle em grupos semisimples sobre corpos locais
AUTOR(ES)
Daniel Miranda Machado
DATA DE PUBLICAÇÃO
2006
RESUMO
Let G be a almost-simple, simply connected and connected Lie group over a local field and S a subsemigroup with non-empty interior. Studying the action of the regular hyperbolic elements in the interior of S on the flag manifold G / P and on the associated euclidean building, we prove the existence and uniqueness of the invariant control set. Moreover we provide a characterization of the set of transitivity of the control sets: the elements of set of transitivity are the fixed points of type w for a regular hyperbolic isometry, where w is a element of the Weyl group of G. Thus, for each w in W there is a control set Dw and W(S) the subgroup of the Weyl group such that the control set Dw coincide with the invariant control set DI is a Weyl subgroup of W. At last, we derived that the control sets are parametrized by the lateral classes W(S)
ASSUNTO(S)
lie semigroups semigrupos grupos de teoria de controle corpos locais (algebra) lie groups control theory
