PORTUGALIAE MATHEMATICA Vol. 60, No. 3, pp. 305317 (2003) 

The Compression Semigroup of a Cone is ConnectedJoao Ribeiro Gonçalves Filho and Luiz A.B. San MartinDepartamento de Matemática, Universidade Estadual de Maringá,87.020900 Maringá Pr  BRASIL Instituto de Matemática, Universidade Estadual de Campinas, Cx. Postal 6065, 13.081970 Campinas SP  BRASIL Abstract: Let $W\subset\R^{n}$ be a pointed and generating cone and denote by $S(W)$ the semigroup of matrices with positive determinant leaving $W$ invariant. The purpose of this paper is to prove that $S(W)$ is path connected. This result has the following consequence: Semigroups with nonempty interior in the group $\mathrm{Sl}(n,\R)$ are classified into types, each type being labelled by a flag manifold. The semigroups whose type is given by the projective space $\P^{n1}$ form one of the classes. It is proved here that the semigroups in $\mathrm{Sl}(n,\R)$ leaving invariant a pointed and generating cone are the only maximal connected in the class of $\P^{n1}$. Keywords: semigroups; convex cones; positive matrices; maximal connected semigroups. Classification (MSC2000): 20M20, 11C20. Full text of the article:
Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.
© 2003 Sociedade Portuguesa de Matemática
