Cones e semigrupos

by Gonçalves Filho, João Ribeiro

Abstract (Summary)
The purpose of this work is to advanced the understanding about the maximalsemigroups with nonempty interior in the speciallinear group Sl(n,R). The compression semigroup of a convex pointed and generating cone form one of the classes of maximal semigroups in the gToup Sl( n, R).Let W C Rn be a pointed and generating cone and form the compression semigroup S(W') of the real matrices with positive determinant leaving W invariant. We prove that S(W) is path connected. Sw = {g E Sl(n,R) : gW C W} is connected too. Also we prove the existence of g in Sl(n,R) such that gVV C -W. So that Sw is not a maximal semigroup. However we get that Sw is a maximal connected semigroup. This informations leave us determinate completely the connected maximal semigroups in Sl( n, R) to n = 2,3.We study the infinitesimal cone L(S(W)) associated to the compression semigroup S (W"). We give a representation of L( S (W"ยป using the moment map of the representation of aLie algebra. To do this we introduce a nilpotent orbit of the action of Sl( n, R) on the tensorial product of the vetorial space V by its dual. We identify this tensorial product with the Lie algebra gl (V) of the linear transformations of V.We also treat the self dual cones and prove some interesting results. Furthermore, we define some other cones in the matrix space, associated to the cone W. Our objetive is introduce new results to help the understanding of the semigroup S(W). We discuss some properties and relations between of these cones
This document abstract is also available in Portuguese.
Bibliographical Information:

Advisor:Luiz Antonio Barrera San Martin; Luiz Antonio Barrera San Martin [Orientador]; Caio Jose Coletti Negreiros; Marcelo Firer; Victor Alberto Jose Ayala Bravo; Washington Luiz Marar

School:Universidade Estadual de Campinas

School Location:Brazil

Source Type:Master's Thesis



Date of Publication:03/09/2001

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