Gonçalves Filho, João Ribeiro; San Martin, Luiz A. B. The compression semigroup of a cone is connected. (English) Zbl 1047.22005 Port. Math. (N.S.) 60, No. 3, 305-317 (2003). Let \(W\subset \mathbb R^n\) be a pointed and generating cone, \(S(W)\) the semigroup of matrices with positive determinant leaving \(W\) invariant. The authors show that \(S(W)\) is path connected. This result has the following consequence: semigroups with nonempty interior in the real special linear group \(Sl(n,\mathbb R)\) are classified into types, each type being labelled by a flag manifold. The semigroups whose type is given by the projective space \(\mathbb P^{n-1}\) form one of the classes. It is also shown here that the semigroups in \(Sl(n,\mathbb R)\) leaving invariant a pointed and generating cone are the only maximal ones connected in the class of \(\mathbb P^{n-1}\). Reviewer: Huang Wenxue (Scarborough) MSC: 22E15 General properties and structure of real Lie groups 15A15 Determinants, permanents, traces, other special matrix functions 20M20 Semigroups of transformations, relations, partitions, etc. Keywords:compression semigroup; convex cones; generating cones; linear transformation semigroup; maximal connected semigroups; pointed cones; positive determinant matrices; special linear group PDFBibTeX XMLCite \textit{J. R. Gonçalves Filho} and \textit{L. A. B. San Martin}, Port. Math. (N.S.) 60, No. 3, 305--317 (2003; Zbl 1047.22005) Full Text: EuDML