Related papers: Lamplighter groups, median spaces, and Hilbertian …

Consider a Grassmannian $\mathrm{Gr}(2, V)$ for an even-dimensional vector space $V$. Its derived category of coherent sheaves has a Lefschetz exceptional collection with respect to the Pl\"ucker embedding. We consider a variety $X_1$ of…

Let $\mathbb{G}$ be the quantum automorphism group of a finite dimensional C*-algebra $(B,\psi)$ and $\Gamma$ a discrete group. We want to compute the fusion rules of $\widehat{\Gamma}\wr_* \mathbb{G}$. First of all, we will revise the…

Given a permutational wreath product sequence of cyclic groups we investigate its minimal generating set, minimal generating set for its commutator and some properties of its commutator subgroup. We strengthen the result of author…

The mixed verbal wreath product in representations of Lie algebras is a construction parallel to the verbal wreath product of Lie algebras introduced by A. L. Shmelkin. It is shown that the analog of the group theorem on embedding in the…

The following refinement of the Higman embedding theorem is proved: A finitely generated group $R$ is recursively presented if and only if there exists a quasi-isometric malnormal embedding of $R$ into a finitely presented group $H$ such…

Let $P \subset \mathbb{R}^{d}$ be a closed convex cone. Assume that $P$ is pointed, i.e. the intersection $P \cap -P=\{0\}$ and $P$ is spanning, i.e. $P-P=\mathbb{R}^{d}$. Denote the interior of $P$ by $\Omega$. Let $E$ be a product system…

Based on a study of the 2-category of weak distributive laws, we describe a method of iterating Street's weak wreath product construction. That is, for any 2-category K and for any non-negative integer n, we introduce 2-categories…

The equivariant and ordinary cohomology rings of Hilbert schemes of points on the minimal resolution C^2//G for cyclic G are studied using vertex operator technique, and connections between these rings and the class algebras of wreath…

If A is an algebra of functions on X, there are many cases when X can be regarded as included in Hom(A,C) as the set of ring homomorphisms. In this paper the corresponding results for the symmetric products of X are introduced. It is shown…

We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications of the main results include a characterization of what finitely presentable groups may admit a…

In this paper, the notion of proper proximality (introduced in [BIP18]) is studied and classified in various families of groups. We show that if a group acts non-elementarily by isometries on a tree such that for any two edges, the…

We study the geometry of compact geodesic spaces with trivial first Betti number admitting large finite groups of isometries. We show that if a finite group $G$ acts by isometries on a compact geodesic space $X$ whose first Betti number…

Permutation products and their various "fat diagonal" subspaces are studied from the topological and geometric point of view. We describe in detail the stabilizer and orbit stratifications related to the permutation action, producing a…

Let $(\Sigma_1,g_1)$ and $(\Sigma_2,g_2)$ be connected, complete and orientable Riemannian two manifolds. Consider the two canonical K\"ahler structures $(G^{\epsilon},J,\Omega^{\epsilon})$ on the product 4-manifold $\Sigma_1\times\Sigma_2$…

A group has finite palindromic width if there exists $n$ such that every element can be expressed as a product of $n$ or fewer palindromic words. We show that if $G$ has finite palindromic width with respect to some generating set, then so…

We show that a wreath product of two finitely generated abelian groups is LERF. Consequently the free metabelian groups are LERF.

We consider the (extended) metaplectic representation of the semidirect product $\mathcal{G}={\mathbb H}^d\rtimes Sp(d,{\mathbb R})$ between the Heisenberg group and the symplectic group. Subgroups $H=\Sigma \rtimes D$, with $\Sigma$ being…

Motivated by the definition of a semigroup compactification of a locally compact group and a large collection of examples, we introduce the notion of an (operator) "homogeneous left dual Banach algebra" (HLDBA) over a (completely…

Every countable group $G$ can be embedded in a finitely generated group $G^*$ that is hopfian and complete, i.e. $G^*$ has trivial centre and every epimorphism $G^*\to G^*$ is an inner automorphism. Every finite subgroup of $G^*$ is…

The Donald--Flanigan problem for a finite group H and coefficient ring k asks for a deformation of the group algebra kH to a separable algebra. It is solved here for dihedral groups and for the classical Weyl groups (whose rational group…