Denote by PSelf Ω (resp., Self Ω) the partial (resp., full) transformation monoid over a set Ω, and by SubV (resp., EndV ) the collection of all subspaces (resp., endomorphisms) of a vector space V . We prove various results that imply the following: (1) If cardΩ > 2, then Self Ω has a semigroup embedding into the dual of Self Γ iff card Γ > 2 . In particular, if Ω has at least two elements, th...

We initiate a parametric study of families of polynomial skew products, i.e., polynomial endomorphisms of C of the form F (z, w) = (p(z), q(z, w)) that extend to endomorphisms of P(C). Our aim is to study and give a precise characterization of the bifurcation current and the bifurcation locus of such a family. As an application, we precisely describe the geometry of the bifurcation current near...

On the bundles of WZW chiral blocks over the moduli space of a punctured rational curve we construct isomorphisms that implement the action of outer automorphisms of the underlying affine Lie algebra. These bundle-isomorphisms respect the Knizhnik--Zamolodchikov connection and have finite order. When all primary fields are fixed points, the isomorphisms are endomorphisms; in this case, the bund...

If f is an endomorphism of a finite dimensional vector space over a field K then an invariant subspace X ⊆ V is called hyperinvariant (respectively, characteristic) if X is invariant under all endomorphisms (respectively, automorphisms) that commute with f . According to Shoda (Math. Zeit. 31, 611–624, 1930) only if |K| = 2 then there exist endomorphisms f with invariant subspaces that are char...