Related papers: Full factors, bicentralizer flow and approximately…

We prove that the normalizer of any diffuse amenable subalgebra of a free group factor $L(\Bbb F_r)$ generates an amenable von Neumann subalgebra. Moreover, any II$_1$ factor of the form $Q \vt L(\Bbb F_r) $, with $Q$ an arbitrary subfactor…

We prove that certain free products of factors of type ${\rm I}$ and other von Neumann algebras with respect to nontracial, almost periodic states are almost periodic free Araki-Woods factors. In particular, they have the free absorption…

We prove a number of results of the following common flavor: for a category $\mathcal{C}$ of topological or uniform spaces with all manner of other properties of common interest (separation / completeness / compactness axioms), a group (or…

Given a countable group G, we consider the sets S_factor(G), S_eqrel(G), of subgroups F of the positive real line for which there exists a free ergodic probability measure preserving action G on X such that the fundamental group of the…

We begin this note with a von Neumann algebraic version of the elementary but extremely useful fact about being able to extend inner-product preserving maps from a total set of the domain Hilbert space to an isometry defined on the entire…

Let $\mathcal{F} $ be a pointwise almost periodic decomposition of a compact metrizable space $X$. Then $\mathcal{F} $ is $R$-closed if and only if $\hat{\mathcal{F}} $ is usc. Moreover, if there is a finite index normal subgroup $H$ of an…

We study the von Neumann algebra, generated by the unitary representations of infinite-dimensional groups nilpotent group $B_0^{\mathbb N}$. The conditions of the irreducibility of the regular and quasiregular representations of…

Let $G$ be a group. The subsets $A_1,\ldots,A_k$ of $G$ form a complete factorization of group $G$ if if they are pairwise disjoint and each element $g\in G$ is uniquely represented as $g=a_1\ldots a_k$, with $a_i\in A_i$. We prove the…

We prove that, for any $t\ge 3$, there exists a constant $c=c(t)>0$ such that any $d$-regular $n$-vertex graph with the second largest eigenvalue in absolute value~$\lambda$ satisfying $\lambda\le c d^{t-1}/n^{t-2}$ contains vertex-disjoint…

W. Arveson has described a cocycle conjugacy class $U(\alpha)$ of $E_0$-semigroup $\alpha$ on B(H) which is a factor of type $\rm I$. Under some conditions on $\alpha$, there is a $E_0$-semigroup $\beta \in U(\alpha)$ being a flow of shifts…

We prove that the approximately inner automorphism group of a separable strongly stable von Neumann algebra is contractible in the u-topology. Thus the automorphism group of the hyperfinite type III_1 factor is contractible.

A certain synchronizing property for subshifts called $\lambda$-synchronization yields $\lambda$-graph systems called the $\lambda$-synchronizing $\lambda$-graph systems for the subshifts. The $\lambda$-synchronizing $\lambda$-graph system…

We extend some results of [BF12] on subfactor projections to show that the projection of a free factor B to the free factor complex of the free factor A is well-defined with uniformly bound diameter, unless either A is contained in B or A…

We prove that any $C^{1+\alpha}$ transitive conservative partially hyperbolic diffeomorphism of a closed 3-manifold with virtually solvable fundamental group is ergodic. Consequently, in light of \cite{FP-classify}, this establishes the…

We introduce the notion of a generalized Jung factor: a II$_1$ factor $M$ for which any two embeddings of $M$ into its ultrapower $M^{\mathcal U}$ are equivalent by an automorphism of $M^{\mathcal U}$. We show that $\mathcal R$ is not the…

We prove that a quasi-finite endomorphism of an algebraic variety over an algebraically closed field of characteristic zero, that is injective on the complement of a closed subvariety, is an automorphism. We also prove that an endomorphism…

In a previous work it is shown that every finite group $G$ of diffeomorphisms of a connected smooth manifold $M$ of dimension $\geq 2$ equals, up to quotient by the flow, the centralizer of the group of smooth automorphisms of a…

We prove that for some manifolds $M$ the set of robustly transitive partially hyperbolic diffeomorphisms of $M$ with one-dimensional nonhyperbolic centre direction contains a $C^1$-open and dense subset of diffeomorphisms with nonhyperbolic…

Let $M$ be a cancellative commutative monoid and call a submonoid $S$ of $M$ an undermonoid if $\G(S)=\G(M)$ inside the Grothendieck group of $M$. Gotti and Li asked whether the finite factorization property is hereditary once it is known…

With every reduced $E$-Fountain semigroup $S$ which satisfies the generalized right ample condition we associate a category with zero morphisms $\mathcal{C}(S)$. Under some assumptions we prove an isomorphism of $\Bbbk$-algebras $\Bbbk…