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Type: Artigo de periódico
Title: Invariant control sets on flag manifolds and ideal boundaries of symmetric spaces
Author: Firer, M
do Rocio, OG
Abstract: Let G be a semisimple real Lie group of non-compact type, K a maximal compact subgroup and S subset of or equal to G a semigroup with nonempty interior. We consider the ideal boundary partial derivative(infinity)(G/K) of the associated symmetric space and the flag manifolds G/P-circle minus. We prove that the asymptotic image partial derivative(infinity)(Sx(0)) subset of or equal to partial derivative(infinity)(G/K), where x(0) is an element of G/K is any given point, is the maximal invariant control set of S in partial derivative(infinity)(G/K). Moreover there is a surjective projection pi : partial derivative(infinity)(Sx(0)) --> Ucircle minussubset of or equal toSigma C-circle minus, where C-circle minus is the maximal invariant control set for the action of S in the flag manifold G/P-circle minus, with P-circle minus a parabolic subgroup. The points that project over C-circle minus are exactly the points of type circle minus in partial derivative(infinity) (Sx(0)) (in the sense of the type of a cell in a Tits Building).
Subject: semigroups
semi-simple Lie groups
control sets
ideal boundary
Country: Alemanha
Editor: Heldermann Verlag
Citation: Journal Of Lie Theory. Heldermann Verlag, v. 13, n. 2, n. 465, n. 479, 2003.
Rights: fechado
Date Issue: 2003
Appears in Collections:Unicamp - Artigos e Outros Documentos

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