Valued Groups.

Locally-finitely-valued Cohomology Groups

Convexly orderable Groups and Valued Fields

We consider the model theoretic notion of convex orderability, which fits strictly between the notions of VC-minimality and dp-minimality. In some classes of algebraic theories, however, we show that convex orderability and VC-minimality are equivalent, and use this to give a complete classification of VC-minimal theories of ordered groups and abelian groups. Consequences for fields are also co...

On Singular Interval-Valued Iteration Groups

Let I = (a,b) and L be a nowhere dense perfect set containing the ends of the interval I and let φ : I → R be a non-increasing continuous surjection constant on the components of I \ L and the closures of these components be the maximal intervals of constancy of . The family F t t R of the interval-valued functions F t 1 φ { , ∈ } (x): = φ [t + φ(x)], x ∈ I forms a set-valued iteration group. W...

Lattice-Valued Quasi-bi-Uniformizability of Lattice-Valued Quasi-bi-Topological Neighborhood Groups

Considering a frame L, we introduce the notions of stratified L-semi-topological neighborhood group, stratified L-quasi-topological neighborhood group, and stratified L-quasi-bi-topological neighborhood group. In so doing, we look at the notion of stratified L-right (left) semi-topological neighborhood group, provide some basic facts, and present a construction of a stratified L-right semi-topo...

A Realization of Quantum Groups via Product Valued Quivers

Let → Γ be a valued quiver. Let C be the symmetrizable generalized Cartan matrix associated to → Γ. We show that the whole quantum group associated to C can be realized from the category of the representations of the product valued quiver → Γ. This method can be used to realize the whole generalized Kac-Moody Lie algebra associated to C, as discussed in [LL].