相关论文: Proper actions of wreath products and generalizati…

Given two finitely generated groups that coarsely embed into a Hilbert space, it is known that their wreath product also embeds coarsely into a Hilbert space. We introduce a wreath product construction for general metric spaces X,Y,Z and…

We show that amenability, the Haagerup property, the Kazhdan's property (T) and exactness are preserved under taking second nilpotent product of groups. We also define the restricted second nilpotent wreath product of groups, this is a…

We prove that the properties of acting metrically properly on some space with walls or some CAT(0) cube complex are closed by taking the wreath product with \Z. We also give a lower bound for the (equivariant) Hilbert space compression of…

The Haagerup property, which is a strong converse of Kazhdan's property $(T)$, has translations and applications in various fields of mathematics such as representation theory, harmonic analysis, operator K-theory and so on. Moreover, this…

We develop a new approach on free wreath products, generalizing the constructions of Bichon and of Fima-Pittau. We show stability properties for certain approximation properties such as exactness, Haagerup property, hyperlinearity and…

By means of analyzing the notion of verbal products of groups, we show that soficity, hyperlinearity, amenability, the Haagerup property, the Kazhdan's property (T) and exactness are preserved under taking $k$-nilpotent products of groups,…

From any two median spaces $X,Y$, we construct a new median space $X \circledast Y$, referred to as the diadem product of $X$ and $Y$, and we show that this construction is compatible with wreath products in the following sense: given two…

We make a comprehensive and self-contained study of compact bicrossed products arising from matched pairs of discrete groups and compact groups. We exhibit an automatic regularity property of such a matched pair and and produce an easy…

For a class of wreath-like product groups with property (T), we describe explicitly all the embeddings between their von Neumann algebras. This allows us to provide a continuum of ICC groups with property (T) whose von Neumann algebras are…

Using recent techniques introduced by Jones we prove that a large family of discrete groups and groupoids have the Haagerup property. In particular, we show that if G is a discrete group with the Haagerup property, then the wreath product…

Given the large class of groups already known to be sofic, there is seemingly a shortfall in results concerning their permanence properties. We address this problem for wreath products, and in particular investigate the behaviour of more…

We characterize the normal extensions of inverse semigroups isomorphic to full restricted semidirect products, and present a Kalouznin-Krasner theorem which holds for a wider class of normal extensions of inverse semigroups than that in the…

If $H$ is a lattice in a locally compact second countable group $G$, then we show that $G$ has property A (respectively is coarsely embeddable into Hilbert space) if and only if $H$ has property A (respectively is coarsely embeddable into…

In this paper we review various strikingly parallel algebraic structures behind Hilbert schemes of points on surfaces and certain finite groups called the wreath products. We explain connections among Hilbert schemes, wreath products,…

We prove some positivity results on the coefficients in the complexified Hilbert polynomial of a semi-stable object. After applying these results on the classical slope stability conditions, we get sequences of quadratic inequalities for…

We define and study a notion of free wreath product with amalgamation for compact quantum groups. These objects were already introduced in the case of duals of discrete groups under the name "free wreath products of pairs" in a previous…

Let $G$ and $H$ be two groups acting on path connected topological spaces $X$ and $Y$ respectively. Assume that $H$ is finite of order $m$ and the quotient maps $p:X\to X/G$ and $q:Y\to Y/H$ are regular coverings. Then it is well-known that…

If $\textbf{S}$ is a subcategory of metric spaces, we say that a group G has property $B\textbf{S}$ if any isometric action on an $\textbf{S}$-space has bounded orbits. Examples of such subcategories include metric spaces, affine real…

In the framework of quantum mechanics over a quadratic extension of the ultrametric field of p-adic numbers, we introduce a notion of tensor product of p-adic Hilbert spaces. To this end, following a standard approach, we first consider the…

We investigate stationarity and stability of half-spaces as isoperimetric sets for product probability measures, considering the cases of coordinate and non-coordinate half-spaces. Moreover, we present several examples to which our results…