Related papers: A strong multiplicity one theorem for dimension da…

For a locally compact group $G$ and a strongly self-absorbing $G$-algebra $(\mathcal{D},\delta)$, we obtain a new characterization of absorption of a strongly self-absorbing action using almost equivariant completely positive maps into the…

Given any countable group $G$, we construct uncountably many quasi-isometry classes of proper geodesic metric spaces with quasi-isometry group isomorphic to $G$. Moreover, if the group $G$ is a hyperbolic group, the spaces we construct are…

Let $\pi=\otimes\pi_{v}$ and $\pi^{\prime}=\otimes\pi_{v}^{\prime}$ be two irreducible, automorphic, cuspidal representations of $GL_{m}(\mathbb{A}_{K}) >.$ Using the logarithmic zero-free region of Rankin-Selberg $L$-function, Moreno…

It is well known that a dense subgroup $G$ of the complex unitary group $U(d)$ cannot be amenable as a discrete group when $d>1$. When $d$ is large enough we give quantitative versions of this phenomenon in connection with certain estimates…

For a finite group $G$, let $B$ be an equivalence (equality, conjugacy or order) relation on $G$ and let $A$ be a (power, enhanced power or commuting) graph with vertex set $G$. The $B$ super $A$ graph is a simple graph with vertex set $G$…

It is known that multiplicity one property holds for SL(2), while the strong multiplicity one property fails. However, in this paper, we show that if we require further that a pair of cuspidal representations $\pi$ and $\pi'$ of SL(2) have…

For every given $p\in [1,+\infty)$ and $n\in\mathbb{N}$ with $n\ge 1$, the authors identify the strong $L^p$-closure $L_{\mathbb{Z}}^p(D)$ of the class of vector fields having finitely many integer topological singularities on a domain $D$…

We generalize two of our previous results on abelian definable groups in $p$-adically closed fields to the non-abelian case. First, we show that if $G$ is a definable group that is not definably compact, then $G$ has a one-dimensional…

Let $H$ be a closed normal subgroup of a compact Lie group $G$ such that $G/H$ is connected. This paper provides a necessary and sufficient condition for every complex representation of $H$ to be extendible to $G$, and also for every…

If a finite group $G$ is isomorphic to a subgroup of $SO(3)$, then $G$ has the D2-property. Let $X$ be a finite complex satisfying Wall's D2-conditions. If $\pi_1(X)=G$ is finite, and $\chi(X) \geq 1-Def(G)$, then $X \vee S^2$ is simple…

Let G be a connected semisimple algebraic group over $k$, with Lie algebra $\g$. Let $\h$ be a subalgebra of $\g$. A simple finite-dimensional $\g$-module V is said to be $\h$-indecomposable if it cannot be written as a direct sum of two…

Almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics are considered. A linear connection $D$ is introduced such that the structure of these manifolds is parallel with respect to D. Of special interest is the class of the…

We consider certain subsets of the space of $n\times n$ matrices of the form $K = \cup_{i=1}^m SO(n)A_i$, and we prove that for $p>1, q \geq 1$ and for connected $\Omega'\subset\subset\Omega\subset \R^n$, there exists positive constant…

We investigate a slight weakening of the classical property of strong approximation, which we call almost strong approximation, for connected reductive algebraic groups over global fields with respect to special sets of valuations. While…

Let $E/F$ be a quadratic extension of non-archimedean local fields of characteristic different from $2$. Let $A$ be an $F$-central simple algebra of even dimension so that it contains $E$ as a subfield, set $G=A^\times$ and $H$ for the…

We explicitly classify all pairs $(M,G)$, where $M$ is a connected complex manifold of dimension $n\ge 2$ and $G$ is a connected Lie group acting properly and effectively on $M$ by holomorphic transformations and having dimension $d_G$…

A visible action on a complex manifold is a holomorphic action that admits a $J$-transversal totally real submanifold $S$. It is said to be strongly visible if there exists an orbit-preserving anti-holomorphic diffeomorphism $\sigma $ such…

A condition, in two variants, is given such that if a property P satisfies this condition, then every logic which is at least as strong as first-order logic and can express P fails to have the compactness property. The result is used to…

High dimensional data can have a surprising property: pairs of data points may be easily separated from each other, or even from arbitrary subsets, with high probability using just simple linear classifiers. However, this is more of a rule…

We generalize the notion of an approximate indicator for a closed subgroup $H$ of a locally compact group $G$ introduced by Aristov, Runde, and Spronk and extend their characterization of the existence of such nets in terms of the…