Related papers: Cocycle conjugacy classes of binary shifts

We give a sufficient condition for two operators to be disjointly frequently hypercyclic. We apply this criterion to composition operators acting on $H(\mathbb D)$ or on the Hardy space $H^2(\mathbb D)$. We simplify a result on disjoint…

Let $G$ be a finite group. We consider the problem of counting simultaneous conjugacy classes of $n$-tuples and simultaneous conjugacy classes of commuting $n$-tuples in $G$. Let $\alpha_{G,n}$ denote the number of simultaneous conjugacy…

We classify irreducible II_1 subfactors A \subset B such that B \ominus A is reducible as an A-A bimodule, with index at most 6+1/5, leaving aside the composite subfactors at index exactly 6. Previous work has already achieved this up to…

We consider H\"older continuous cocycles over an accessible partially hyperbolic system with values in the group of diffeomorphisms of a compact manifold $M$. We obtain several results for this setting. If a cocycle is bounded in…

We show that if there exists a countable Borel equivalence relation which is hyper-hyperfinite but not hyperfinite then the complexity of hyperfinite countable Borel equivalence relations is as high as possible, namely,…

We prove that under fairly general conditions an iterated exchange move gives infinitely many non-conjugate braids. As a consequence, every knot has infinitely many conjugacy classes of n-braid representations if and only if it has one…

We classify the bireflections (products of 2 involutions) in the commutator subgroup G an orthogonal group O(V) over a finite field GF(q) of characteristic not 2. We show that every element of G is a bireflection if it is reversible…

We give a characterization of a finite-dimensional commuting square of C*-algebras with a normalized trace that produces a hyperfinite type II_1 subfactor of finite index and finite depth in terms of Morita equivalent unitary fusion…

We study common frequently hypercyclic vectors for countable families of weighted backward shifts acting on $\ell_p$ spaces, $1\leq p<\infty$. Using probabilistic techniques, we develop a general existence criterion, complemented by a…

The authors conjectured previously that a knot is nonfibered if and only if its infinite cyclic cover has uncountably many finite covers. We prove the conjecture for a class of knots that includes all knots of genus 1, using techniques from…

We extend a result of B\`{e}s, Martin, Peris and Shkarin by stating: $B_w$ is $\mathscr{F}$-weighted backward shift if and only if $(B_w,\dots, B_w^r)$ is $d$-$\mathscr{F}$, for any $r\in \mathbb{N}$, where $\mathscr{F}$ runs along some…

We call a subfactor trivial if it is isomorphic with the obvious inclusion of N into matrices over N. We prove the existence of type II_1 factors M without non-trivial finite index subfactors. Equivalently, every M-M-bimodule with finite…

We will introduce the Rohlin property for flows on von Neumann algebras and classify them up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as Kawahigashi's classification of flows on…

Let $I$ be a countably infinite index set, and let $X$ be a Banach sequence space over $I.$ In this article, we characterize disjoint hypercyclic and supercyclic weighted pseudo-shift operators on $X$ in terms of the weights, the OP-basis,…

This paper gives a definitive solution to the problem of describing conjugacy classes in arbitrary Coxeter groups in terms of cyclic shifts. Let $(W,S)$ be a Coxeter system. A cyclic shift of an element $w\in W$ is a conjugate of $w$ of the…

Let ${\cal C}$ be a nonempty class of finite groups closed under taking subgroups, homomorphic images and extensions. A subgroup $H$ of an abstract residually ${\cal C}$ group $R$ is said to be conjugacy ${\cal C}$-distinguished if whenever…

Let $G$ be a profinite group. We prove that the commutator subgroup $G'$ is finite-by-procyclic if and only if the set of all commutators of $G$ is contained in a union of countably many procyclic subgroups.

The classification of homogeneous scalar weighted shifts is known. Recently, Kor\'{a}nyi obtained a large class of inequivalent irreducible homogeneous bi-lateral $2$-by-$2$ block shifts. In this paper, we construct two distinct classes of…

There is a well-known classification of conjugacy classes of involutions in finite Coxeter groups, in terms of subsets of nodes of their Coxeter graphs. In many cases, the product of an involution with the longest element is again an…

We determine the subfactors $N\subset R$ of the hyperfinite $II_1$-factor R with finite index for which the $C^*$-tensor category of the associated $(N,N)$-bimodules is equivalent to the $C^*$-tensor category $\C{U}_G$ of all unitary finite…