Related papers: Compact Group Actions on Topological and Noncommut…

We discuss a possible noncommutative generalization of the notion of an equivariant vector bundle. Let $A$ be a $\mathbb{K}$-algebra, $M$ a left $A$-module, $H$ a Hopf $\mathbb{K}$-algebra, $\delta:A\to H\otimes A:=H\otimes_{\mathbb{K}} A$…

Let $M$ be a closed, connected, orientable topological four-manifold with $H_1(M)$ nontrivial and free abelian, $b_2(M)\ne 0, 2$, and $\chi(M)\ne 0$. We show that if $G$ is a finite group of 2-rank $\le 1$ which admits a homologically…

We prove an analogue of the Baum-Connes conjecture for free orthogonal quantum groups. More precisely, we show that these quantum groups have a $ \gamma $-element and that $ \gamma = 1 $. It follows that free orthogonal quantum groups are $…

Let $G$ and $A$ be finite groups with $A$ acting on $G$ by automorphisms. In this paper we introduce the concept of "good action"; namely we say the action of $A$ on $G$ is good, if $H=[H,B]C_H(B)$ for every subgroup $B$ of $A$ and every…

We prove that if a subgroup $H$ of the automorphism group $\mathrm{Aut}(\Sigma^{\mathbb{Z}})$ of a non-trivial full shift acts on points of finite support with a free orbit, then for every finitely-generated abelian group $A$, the abstract…

We study the topological dynamics of the action of an acylindrically hyperbolic group on the space of its infinite index convex cocompact subgroups by conjugation. We show that, for any suitable probability measure $\mu$, random walks with…

Let A be a commutative unital algebra over an algebraically closed field k of characteristic not equal to 2, whose generators form a finite-dimensional subspace V, with no nontrivial homogeneous quadratic relations. Let Q be a Hopf algebra…

Given an extension $0\to V\to G\to Q\to1$ of locally compact groups, with $V$ abelian, and a compatible essentially bijective $1$-cocycle $\eta\colon Q\to\hat V$, we define a dual unitary $2$-cocycle on $G$ and show that the associated…

A Hom-group is the non-associative generalization of a group, whose associativity and unitality are twisted by a compatible bijective map. In this paper, we give some new examples of Hom-groups, and show the first and the second isomorphism…

Let $G$ be a totally disconnected, locally compact group and let $H$ be a virtually flat (for example, polycyclic) group of automorphisms of $G$. We study the structure of, and relationships between, various subgroups of $G$ defined by the…

A (non-commutative) Ulam quasimorphism is a map $q$ from a group $\Gamma$ to a topological group $G$ such that $q(xy)q(y)^{-1}q(x)^{-1}$ belongs to a fixed compact subset of $G$. Generalizing the construction of Barge and Ghys, we build a…

We provide and study an equivariant theory of group (co)homology of a group G with coefficients in a gamma-equivariant G-module A, when a separate group "gamma" acts on G and A, generalizing the classical Eilenberg-MacLane (co)homology of…

For a large class of word hyperbolic groups G the cross product C^*-algebra arising from the action of G on its Gromov boundary is shown to satisfy Poincare duality in K-theory. This class strictly contains fundamental groups of compact,…

Let $H$ be a real algebraic group acting equivariantly with finitely many orbits on a real algebraic manifold $X$ and a real algebraic bundle $\mathcal{E}$ on $X$. Let $\mathfrak{h}$ be the Lie algebra of $H$. Let…

We give local upper and lower bounds for the eigenvalues of the modular operator associated to an ergodic action of a compact quantum group on a unital C*-algebra. They involve the modular theory of the quantum group and the growth rate of…

Using topological notions of translation-like actions introduced by Schneider, we give a positive answer to a geometric version of Burnside problem for locally compact group. The main theorem states that a locally compact group is…

Commutative shuffle products are known to be intimately related to universal formulas for products, exponentials and logarithms in group theory as well as in the theory of free Lie algebras, such as, for instance, the…

We construct the join of noncommutative Galois objects (quantum torsors) over a Hopf algebra H. To ensure that the join algebra enjoys the natural (diagonal) coaction of H, we braid the tensor product of the Galois objects. Then we show…

In combinatorial problems it is sometimes possible to define a $G$-equivariant mapping from a space $X$ of configurations of a system to a Euclidean space $\mathbb{R}^m$ for which a coincidence of the image of this mapping with an…

In this paper we first consider the Hamiltonian action of a compact connected Lie group on an $H$-twisted generalized complex manifold $M$. Given such an action, we define generalized equivariant cohomology and generalized equivariant…