Related papers: On fields of definition of arithmetic Kleinian ref…

We consider indecomposable representations of the Klein four group over a field of characteristic $2$ and of a cyclic group of order $pm$ with $p,m$ coprime over a field of characteristic $p$. For each representation we explicitly describe…

Using a new powerful technique based on the notion of megaideal, we construct a complete set of inequivalent realizations of real Lie algebras of dimension no greater than four in vector fields on a space of an arbitrary (finite) number of…

This paper is designed to attract people who work on real hyperbolic manifolds to consider thinking about discrete subgroups of higher rank Lie groups. To that end, we breezily discuss some applications of the ideas from the theory of…

Let $K$ be a number field. We present several new finiteness results for isomorphism classes of abelian varieties over $K$ whose $\ell$-power torsion fields are arithmetically constrained for some rational prime $\ell$. Such arithmetic…

We consider the computational problem of determining the unit group of a finite ring, by which we mean the computation of a finite presentation together with an algorithm to express units as words in the generators. We show that the problem…

We investigate the finite subgroups that occur in the Hamiltonian quaternion algebra over the real subfield of cyclotomic fields. When possible, we investigate their distribution among the maximal orders.

This paper introduces two classes of totally real quartic number fields, one of biquadratic extensions and one of cyclic extensions, each of which has a non-principal Euclidean ideal. It generalizes techniques of Graves used to prove that…

The finite-dimensional restricted simple Lie algebras of characteristic p > 5 are classical or of Cartan type. The classical algebras are analogues of the simple complex Lie algebras and have a well-advanced representation theory with…

Motivated by the theory of graph limits, we introduce and study the convergence and limits of linear representations of finite groups over finite fields. The limit objects are infinite dimensional representations of free groups in…

In this paper, we present a complete classification of all imaginary $n$-quadratic fields of class number 1.

We present a technique for rendering limit sets for kleinian groups, based upon the base transformation of integers and which aims at saving memory resources and being faster than the traditional dictionary based approach.

The aim of this paper is to describe all definable subgroups of SL2(K), for K a p-adically closed field. We begin by giving some "frame subgroups" which contain all nilpotent or solvable subgroups of SL2(K). A complete description is givien…

We present a framework to determine subgroups of tetrahedron groups and tetrahedron Kleinian groups, based on tools in color symmetry theory.

We obtain tight bounds for the minimal number of generators of an ideal with bounded-degree generators in a polynomial ring $K[X_1,\dots,X_n],$ as well as a sharp quantification of the maximum possible size of a minimal generating set of…

In this paper we introduce and study the relative cyclic subgroup commutativity degrees of a finite group. We show that there is a finite group with $n$ such degrees for all $n \in \mathbb{N}^*\setminus \lbrace 2\rbrace$ and we indicate…

The goal of this paper is to present some results and (more importantly) state a number of conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products categorifies certain structures in the…

We give some bounds on the numbers of rational points on abelian varieties and jacobians varieties over finite fields. The main result is that we determine the maximum and minimum number of rational points on jacobians varieties of…

For an arbitrary representation $\rho$ of a complex finite-dimensional Lie algebra, we construct a collection of numbers that we call the Jordan-Kronecker invariants of $\rho$. Among other interesting properties, these numbers provide lower…

We describe the two-generated limits of abelian-by-(infinite cyclic) groups in the space of marked groups using number theoretic methods. We also discuss universal equivalence of these limits.

We define Lie subalgebras of the group algebra of a finite pseudo-reflection group that are involved in the definition of the Cherednik KZ-systems, and determine their structure. We provide applications for computing the Zariski closure of…