Irreducible semigroups of matrices with eigenvalue one
The authors study complex \(n\times n\) matrix groups and semigroups with the property that each matrix acting on \(\mathbb C^n\) has a fixed point, or, equivalently has an eigenvalue one. It is shown that for \(4\neq n\geq 3\) there are irreducible matrix groups and irreducible semigroups of nonnegative matrices with this property. In particular, for \(n=3\), the structure of any such semigroup is determined. The authors also present additional hypotheses that imply reducibility.
scientific article; zbMATH DE number 2051545