Related papers: Conjugacy co-amenability

We present an axiomatic approach to combination theorems for various homological properties of groups and, more generally, of chain complexes. Examples of such properties include algebraic finiteness properties, $\ell^2$-invisibility,…

For a discrete group $G$, we consider certain ideals $\mathcal{I}\subset c_0(G)$ of sequences with prescribed rate of convergence to zero. We show that the equality between the full group C$^\ast$-algebra of $G$ and the C$^\ast$-completion…

We study the algebra $\mathfrak{M}^{\infty,\mathrm{dec}}(G)$ of decomposable Fourier multipliers on the group von Neumann algebra $\mathrm{VN}(G)$ of a locally compact group $G$, and its relation to the Fourier-Stieltjes algebra…

In a previous paper the authors developed an operator-algebraic approach to Lewis Bowen's sofic measure entropy that yields invariants for actions of countable sofic groups by homeomorphisms on a compact metrizable space and by…

We study the operator-valued partial derivative associated with covariance matrices on a von Neumann algebra B. We provide a cumulant characterization for the existence of conjugate variables and study some structure implications of their…

Relative property (T) has recently been used to construct a variety of new rigidity phenomena, for example in von Neumann algebras and the study of orbit-equivalence relations. However, until recently there were few examples of group pairs…

For $G$ a finite group, let $\kappa(G)$ be the probability that $\sigma,\tau\in G$ are conjugate, when $\sigma$ and $\tau$ are chosen independently and uniformly at random. In this paper, we extend the methods of Blackburn et al [2012] to…

The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a…

Let G denote a connected, quasi-split reductive group over a field F that is complete with respect to a discrete valuation and that has a perfect residue field. Under mild hypotheses, we produce a subset of the Lie algebra g(F) that picks…

The Haagerup property for locally compact groups is generalised to the context of locally compact quantum groups, with several equivalent characterisations in terms of the unitary representations and positive-definite functions established.…

We introduce the weak Haagerup property for locally compact groups and prove several hereditary results for the class of groups with this approximation property. The class contains a priori all weakly amenable groups and groups with the…

We show that coincidence of the full and reduced crossed product $C^\ast$-algebras of a group action on a unital commutative $C^\ast$-algebra implies amenability of the action whenever the group is exact. This is a partial answer to a…

In physics, entanglement 'reduces' the entropy of an entity, because the (von Neumann) entropy of, e.g., a composite bipartite entity in a pure entangled state is systematically lower than the entropy of the component sub-entities. We show…

Using the strong relation between coactions of a discrete group G on C*-algebras and Fell bundles over G, we prove a new version of Mansfield's imprimitivity theorem for coactions of discrete groups. Our imprimitivity theorem works for the…

The paper is devoted to the investigation of Segal's entropy in semifinite von Neumann algebras. The following questions are dealt with: semicontinuity, the 'ideal-like' structure of the linear span of the set of operators with finite…

We develop a version of quantum mechanics that can handle nonassociative algebras of observables and which reduces to standard quantum theory in the traditional associative setting. Our algebraic approach is naturally probabilistic and is…

We investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, L1(G), and the Fourier algebra, A(G), of a locally compact group, G.

The additivity with respect to exact sequences is notoriously a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by deeply exploiting their structure. On the other hand, a solvable…

This book is concerned with analytic approaches of studying groups and their actions. Much attention is devoted to the study of amenability and Kazhdan's property (T), which are perhaps the most important analytic properties of a group, but…

For every countable abelian group $G$ we find the set of all its subgroups $H$ ($H\leq G$) such that a typical measure-preserving $H$-action on a standard atomless probability space $(X,\mathcal{F}, \mu)$ can be extended to a free…