Related papers: Affine Extensions of loops

We consider interpretable topological spaces and topological groups in a $p$-adically closed field $K$. We identify a special class of "admissible topologies" with topological tameness properties like generic continuity, similar to the…

We call a unital locally convex algebra $A$ a continuous inverse algebra if its unit group $A^\times$ is open and inversion is a continuous map. For any smooth action of a, possibly infinite-dimensional, connected Lie group $G$ on a…

Let G be a connected semisimple Lie group such that the associated symmetric space X is Hermitian and let Gamma be the fundamental group of a compact orientable surface of genus at least 2. We survey the study of maximal representations,…

Let $A$ be an elementary abelian $r$-group with rank at least $3$ that acts faithfully on the finite $r'$-group $G$. Assume that $G$ is $A$-simple, so that $G = K_{1} \times\cdots\times K_{n}$ where $K_{1},\ldots,K_{n}$ is a collection of…

This paper introduces a description of Endomorphisms of the translation group in an affine plane, will define the addition and composition of the set of endomorphisms and specify the neutral elements associated with these two actions and…

In this note we establish the following result (announced in a previous work): if a linear group is the image of a representation of a K\"ahler group, then it has a finite index subgroup which is the image of a representation of the…

We study amenability of affine algebras (based on the notion of almost-invariant finite-dimensional subspace), and apply it to algebras associated with finitely generated groups. We show that a group G is amenable if and only if its group…

Let $F$ be a local non-archimedian field of positive characteristic, $D$ be a skew-field with center $F$ and $ G=D^{\star}$ be the multiplicative group of $D$. The goal of this paper is to provide a canonical decomposition of any complex…

Let $\Gamma$ be either i) the absolute Galois group of a local field $F$, or ii) the topological fundamental group of a closed connected orientable surface of genus $g$. In case i), assume that $\mu_{p^2} \subset F$. We give an elementary…

We study holomorphic foliations with an affine homogeneous transverse structure. We give a friendly characterization of the case of transversely affine foliations in terms of matrix valued pairs of differential forms. This leads naturally…

We will give an explicit construction of irreducible suparcuspidal representations of the special linear group over a non-archimedean local field and will speculate its Langlands parameter by means of verifying the Hiraga-Ichino-Ikeda…

For a connected smooth projective curve $X$ of genus $g$, global sections of any line bundle $L$ with $\deg(L) \geq 2g+ 1$ give an embedding of the curve into projective space. We consider an analogous statement for a Berkovich skeleton in…

We show how to construct unitary dual $2$-cocycles for a class of semidirect products that exhibit many similarities with the affine group ${\rm Aff}(V)=\GL(V)\ltimes V$ of a finite dimensional vector space over a local skew field. The…

We develop a theory of additive group actions on affine ind-schemes through a purely algebraic and topological framework. Affine ind-schemes are described via complete, second-countable, linearly topologized rings, and actions of the…

We introduce the notion of a contractible subshift. This is a strengthening of the notion of strong irreducibility, where we require that the gluings are given by a block map. We show that a subshift is a retract of a full shift if and only…

For any finite group $G$, and any positive integer $n$, we construct an association scheme which admits the diagonal group $D_n(G)$ as a group of automorphisms. The rank of the association scheme is the number of partitions of $n$ into at…

The affine Grassmannian associated to a reductive group $\mathbf{G}$ is an affine analogue of the usual flag varieties. It is a rich source of Poisson varieties and their symplectic resolutions. These spaces are examples of conical…

Let $T_n(q)$ be the ring of lower triangular matrices of order $n \geq 2$ with entries from the finite field $F(q)$ of order $q \geq 2$ and let ${^2T_n(q)}$ denote its free left module. For $n=2,3$ it is shown that the projective line over…

Given a group $G$ and a number field $K$, the Grunwald problem asks whether given field extensions of completions of $K$ at finitely many places can be approximated by a single field extension of $K$ with Galois group G. This can be viewed…

The article provides a sufficient condition for a locally finite module over the absolute Galois group of a finite field F to satisfy the Riemann Hypothesis Analogue with respect to the projective line. The condition holds for all smooth…