Related papers: Algebraic expansivity on abelian groups

The aim of this paper is to explore non-abelian extensions of Bol algebras and to study the extensibility of a pair of automorphisms within these non-abelian extensions. We begin by researching non-abelian extensions of Bol algebras and…

Let $C,A$ be countable abelian groups. In this paper we determine the complexity of classifying extensions $C$ by $A$, in the cases when $C$ is torsion-free and $A$ is a $p$-group, a torsion group with bounded primary components, or a free…

We consider expansive group actions on a compact metric space containing a special fixed point denoted by $0$, and endomorphisms of such systems whose forward trajectories are attracted toward $0$. Such endomorphisms are called…

In this paper, for given an algebraic theory $T$ whose category $C$ of models is semi-abelian, we consider the topological models of $T$ called topological $T$-algebras and obtain some results related to the fundamental groups of…

A self-contained description of algebraic structures, obtained by combinations of various limit procedures applied to vertex and face sl(2) elliptic quantum affine algebras, is given. New double Yangians structures of dynamical type are in…

It is well-known that abelian varieties are projective, and so that there exist explicit polynomial and rational functions which define both the variety and its group law. It is however difficult to find any explicit polynomial and rational…

The main goal of the article is to study the Pontryagin duality for Abelian $s$- and $sb$-groups. Let $G$ be an infinite Abelian group and $X$ be the dual group of the discrete group $G_d$. We show that a dense subgroup $H$ of $X$ is…

In this article we consider some questions raised by F. Benoist, E. Bouscaren and A. Pillay. We prove that infinitely $p$-divisible points on abelian varieties defined over function fields of transcendence degree one over a finite field are…

We survey recent results on multiple transitivity of automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the…

Double coverings of the orthogonal groups of the real and complex spaces are considered. The relation between discrete transformations of these spaces and fundamental automorphisms of Clifford algebras is established, where an isomorphism…

We describe all the quasi-bialgebra structures of a group algebra over a torsion-free abelian group. They all come out to be triangular in a unique way. Moreover, up to an isomorphism, these quasi-bialgebra structures produce only one…

We explore the relationship between a certain "abelian duality" property of spaces and the propagation properties of their cohomology jump loci. To that end, we develop the analogy between abelian duality spaces and those spaces which…

We generalize the prequantization central extension of a group of diffeomorphisms preserving a closed 2-form \omega (\omega-invariant diffeomorphisms) to an abelian extension of a group of diffeomorphisms preserving a closed vector valued…

We introduce a new class of Abelian groups which lies strictly between the classes of co-Hopfian groups and Dedekind-finite groups, calling these groups {\it Bassian-finite}. We prove the surprising fact that in the torsion case the…

We exhibit infinite, solvable, virtually abelian groups with a fixed number of generators, having arbitrarily large balls consisting of torsion elements. We also provide a sequence of 3-generator non-virtually nilpotent polycyclic groups of…

We consider gerenalizated permutation equivalence of Vielenkin system on commutative compact torsion finite exponent groups.

We establish a link between abelian regular subgroup of the affine group, and commutative, associative algebra structures on the underlying vector space that are (Jacobson) radical rings. As an application, we show that if the underlying…

We study endomorphism rings of principally polarized abelian surfaces over finite fields from a computational viewpoint with a focus on exhaustiveness. In particular, we address the cases of non-ordinary and non-simple varieties. For each…

Let $G$ be the group of all $\ZZ$-valued homomorphisms of the Baer-Specker group $\ZZ^\NN$. The group $G$ is algebraically isomorphic to $\ZZ^{(\NN)}$, the infinite direct sum of the group of integers, and equipped with the topology of…

In this paper we begin the systematic study of group equations with abelian predicates in the main classes of groups where solving equations is possible. We extend the line of work on word equations with length constraints, and more…