Assuming the continuum hypothesis, we construct a pure subgroup G of the Baer-Specker group Z0 with the following properties. Every endomorphism of G differs from a scalar multiplication by an endomorphism of finite rank. Yet G has uncountably many homomorphisms to Z.

Let $X$ be a normal compact K\"ahler space of dimension $n$. A surjective endomorphism $f$ such is int-amplified if $f^*\xi-\xi=\eta$ for some classes $\xi$ and $\eta$. First, we show that this definition generalizes the notion in projective setting. Second, prove cases being smooth, surface or threefold with mild singularities, admits an pseudo-effective canonical divisor, then it $Q$-torus. F...

that is both analytic (as a mapping of complex manifolds) and algebraic: addition of points in E(C) corresponds to addition in C modulo the lattice L. This correspondence between lattices and elliptic curves over C is known as the Uniformization Theorem; we will spend this lecture and part of the next proving it. To make the correspondence explicit, we need to specify the map Φ from C/L and an ...

Endomorphism algebras gure prominently in group representation theory. F or example, if G is a nite group of Lie type, the representation theory of the endomorphism algebra End G Cj G B |sometimes known as the Hecke algebra over C of G|plays a central role in unraveling the complex unipotent c haracters on G 22, 77. Another example arises in the modular representation theory of the nite general...

Endomorphism monoids have long been of interest in universal algebra and also in the study of particular classes of algebraic structures. For any algebra, the set of endomorphisms is closed under composition and forms a monoid (that is, a semigroup with identity). The endomorphism monoid is an interesting structure from a given algebra. In this thesis we study the structure and properties of th...

A subtheory of a quantum eld theory speciies von Neumann subalgebras A(O) (thèob-servables' in the space-time region O) of the von Neumann algebras B(O) (thèèlds ' localized in O). Every local algebra being a (type III 1) factor , the inclusion A (O) B (O) is a sub-factor. The assignment of these local subfactors to the space-time regions is called a ` net of subfactors '. The theory of subfact...