Related papers: Weak mixing for compact Lie extensions of interval…

Let $T=(T_t^f)_{t\in \mathbb{R}}$ be a special flow built over an IET $T : T \to T$ of bounded type, under a roof function f with symmetric logarithmic singularities at a subset of discontinuities of T. We show that $T$ satisfies so-called…

We study some generalizations of the notion of regular crossed products K*G. For the case when K is an algebraically closed field, we give necessary and sufficient conditions for the twisted group ring K*G to be an n-weakly regular ring, a…

We answer positively a question of Ryzhikov, namely we show that being a relatively weakly mixing extension is a comeager property in the Polish group of measure preserving transformations. We study some related classes of ergodic…

We obtain a mixed complex simpler than the canonical one the computes the type cyclic homologies of a crossed product with invertible cocycle $A\times_{\rho}^f H$, of a weak module algebra $A$ by a weak Hopf algebra $H$. This complex is…

It is proved that each Gaussian cocycle over a mildly mixing Gaussian transformation is either a Gaussian coboundary or sharply weak mixing. The class of nonsingular infinite direct products $T$ of transformations $T_n$, $n\in\Bbb N$, of…

The article addresses some open questions about the relations between the topological weak mixing property and the transitivity of the map $f\times f^2 \times...\times f^m$, where $f\colon X\ra X$ is a topological dynamical system on a…

Let V be a vertex operator algebra, and for k a positive integer, let g be a k-cycle permutation of the vertex operator algebra V^{\otimes k}. We prove that the categories of weak, weak admissible and ordinary g-twisted modules for the…

In this paper we present the general theory of cleft extensions for a cocommutative weak Hopf algebra $H$. For a weak left $H$-module algebra we obtain a bijective correspondence between the isomorphisms classes of $H$-cleft extensions…

We consider suspension flows built over interval exchange transformations with the help of roof functions having an asymmetric logarithmic singularity. We prove that such flows are strongly mixing for a full measure set of interval exchange…

A new highly symmetrical model of the compact Lie algebra $\mathfrak{g}^c_2$ is provided as a twisted ring group for the group $\mathbb{Z}_2^3$ and the ring $\mathbb{R}\oplus\mathbb{R}$. The model is self-contained and can be used without…

Let $G$ be a semi-direct product $G=A\times_\phi K$ with $A$ Abelian and $K$ compact. We characterize spread-out probability measures on $G$ that are mixing by convolutions by means of their Fourier transforms. A key tool is a spectral…

We define a stronger property than unique ergodicity with respect to the fixed-point subalgebra previously investigated by Abadie and Dykema. Such a property is denoted as F-strict weak mixing (F stands for the Markov projection onto the…

If $\alpha$ is an amenable action of a discrete group $G$ on a unital C*-algebra $A$, then the crossed-product C*-algebra $A\rtimes_\alpha G$ has the weak expectation property if and only if $A$ has this property.

The concept of weak Lie motion (weak Lie symmetry) is introduced through ${\cal{L}}_{\xi}{\cal{L}}_{\xi}g_{ab}=0,$ (${\cal{L}}_{\xi}{\cal{L}}_{\xi}f=0$). Applications are given which exhibit a reduction of the usual symmetry, e.g., in the…

We define an infinite measure-preserving transformation to have infinite symmetric ergodic index if all finite Cartesian products of the transformation and its inverse are ergodic, and show that infinite symmetric ergodic index does not…

Let G be a finite abelian group. We will consider a skew product extension of a product of two Cantor minimal Z-systems associated with a G-valued cocycle. When G is non-cyclic and the cocycle is non-degenerate, it will be shown that the…

We prove a number of results on the survival of the type-I property under extensions of locally compact groups: (a) that given a closed normal embedding $\mathbb{N}\trianglelefteq\mathbb{E}$ of locally compact groups and a twisted action…

Let $G$ be a noncompact real algebraic group and $\G<G$ a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of $G$ or $\G$ on a compact manifold which admits a smooth deformation. We…

The weak mean equicontinuous properties for a countable discrete amenable group $G$ acting continuously on a compact metrizable space $X$ are studied. It is shown that the weak mean equicontinuity of $(X \times X,G)$ is equivalent to the…

We produce affine interval exchange transformations (AIETs) which are topologically conjugated to (standard) interval exchange maps (IETs) via a singular conjugacy, i.e. a diffeomorphism $h$ of $[0,1]$ which is $C^0$ but not $C^1$ and such…