Related papers: Multiplication of Weak Equivalence Classes May Be …

Let $\Gamma$ be a lattice in a simply connected nilpotent Lie group $G$. Given an infinite measure preserving action $T$ of $\Gamma$ and a "direction" in $G$ (i.e. an element $\theta$ of the projective space $P(\goth g)$ of the Lie algebra…

Let $W$ be a domain in a connected complex manifold $M$ and $w_0\in W$. Let ${\mathcal A}_{w_0}(W,M)$ be the space of all continuous mappings of a closed unit disk $\overline D$ into $M$ that are holomorphic on the interior of $\overline…

We show that, assuming the existence of $\mathfrak{c}$ incomparable selective ultrafilters, there exists a Wallace semigroup whose infinite countable power is the least power which fails to be countably compact. This answers positively…

Let $V$ be a finite-dimensional unitary representation of a compact quantum group $\mathrm{G}$ and denote by $\mathrm{G}_W$ the isotropy subgroup of a linear subspace $W\le V$ regarded as a point in the Grassmannian $\mathbb{G}(V)$. We show…

Let $(X,\Gamma)$ be a topological system, where $\Gamma$ is a nilpotent group generated by $T_1,\ldots, T_d$ such that for each $T\in \Gamma$, $T\neq e_\Gamma$, $(X,T)$ is weakly mixing and minimal. For $d,k\in \mathbb{N}$, let $p_{i,j}(n),…

Let $G$ be a noncompact semisimple algebraic group with trivial center, $S < G$ a maximal split torus, $H < G$ the centralizer of $S$ in $G$ and $\Gamma < G$ an irreducible lattice. Consider the group measure space von Neumann algebra…

We study exact sequences of finite tensor categories of the form $\Rep G \to \C \to \D$, where $G$ is a finite group. We show that, under suitable assumptions, there exists a group $\Gamma$ and mutual actions by permutations $\rhd: \Gamma…

Let $\Gamma$ be a finitely generated group, and let $\mu$ be a nondegenerate, finitely supported probability measure on $\Gamma$. We show that every co-compact $\Gamma$ action on a locally compact Hausdorff space admits a nonzero…

We show that if $\Gamma\curvearrowright (X^\Gamma,\mu^\Gamma)$ is a Bernoulli action of an i.c.c. nonamenable group $\Gamma$ which is weakly amenable with Cowling-Haagerup constant $1$, and $\Lambda\curvearrowright(Y,\nu)$ is a free ergodic…

Let $\mathfrak{g}$ be a simple Lie algebra over $\mathbb{C}$ and $G$ be the corresponding simply connected algebraic group. Consider a nilpotent element $e\in \mathfrak{g}$, the corresponding element $\chi=(e, \bullet)$ in $\mathfrak{g}^*$,…

Let $M$ be a Hopf--von Neuman algebra with the predual $M_*$ and $WAP(M)$ the subspace in $M$ composed of weakly almost periodic functionals on $M_*$. The main example of such an algebra is $M=L^\infty(\mathbb G)$ for a locally compact…

This paper includes a series of structural results for von Neumann algebras arising from measure preserving actions by product groups on probability spaces. Expanding upon the methods used earlier by the first two authors \cite{CS}, we…

A lifting of a semilattice S is an algebra A such that the semilattice of compact (=finitely generated) congruences of A is isomorphic to S. The aim of this work is to give a categorical theory of partial algebras endowed with a partial…

A map $f:X\to Y$ between topological spaces is called weakly discontinuous if each subspace $A\subset X$ contains an open dense subspace $U\subset A$ such that the restriction $f|U$ is continuous. A bijective map $f:X\to Y$ between…

Using percolation techniques, Gaboriau and Lyons recently proved that every countable, discrete, nonamenable group $\Gamma$ contains measurably the free group $\mathbf F_2$ on two generators: there exists a probability measure-preserving,…

Let $\Gamma$ be a finitely generated group acting properly discontinuously by isometries on a visibility CAT(0) space $X$ that satisfies the bounded packing property. We prove that $\Gamma$ satisfies the Tits alternative: it is either…

In this short article, we study the extremal behavior $F_\Gamma(n)$ of divisibility functions $D_\Gamma$ introduced by the first author for finitely generated groups $\Gamma$. We show finitely generated subgroups of $\GL(m,K)$ for an…

Every countable directed graph generates a Fock space Hilbert space and a family of partial isometries. These operators also arise from the left regular representations of free semigroupoids derived from directed graphs. We develop a…

Let $M$ be a finite von Neumann algebra. In the first part, we give asymptotic results about $M$-stable sequences of weak*-continuous mappings which are related with operators belonging to $M$. In the second part, we extend, by a shorter…

Let $\Gamma$ be a group which is virtually free of rank at least 2 and let $\mathcal{F}_{td}(\Gamma)$ be the family of totally disconnected, locally compact groups containing $\Gamma$ as a co-compact lattice. We prove that the values of the…