相关论文: Maximal abelian subalgebras of the group factor of…

Using computations in the bidual of $\mathbb{B}(L^2M)$ we develop a new technique at the von Neumann algebra level to upgrade relative proper proximality to full proper proximality. This is used to structurally classify subalgebras of…

In this two part work we prove that for every finitely generated subgroup $\Gamma < \text{Out}(F_n)$, either $\Gamma$ is virtually abelian or $H^2_b(\Gamma;\mathbb{R})$ contains an embedding of $\ell^1$. The method uses actions on…

A maximal abelian normal subgroup A in a nilpotent group N is self-centralizing. This makes their role an important one in determining the structure of the nilpotent group. For example if A is finite then N is also finite. In the free…

Let $X$ be the $2$-sphere $\mathbb S^2$ or the real projective plane $\mathbb {RP}^2$. We show that if $\Gamma$ is a finitely generated group acting minimally and distally on $X$, then $\Gamma$ contains a nonabelian free subgroup.

In this paper we develop the theory of strongly singular subalgebras of von Neumann algebras, begun in earlier work. We mainly examine the situation of type $\tto$ factors arising from countable discrete groups. We give simple criteria for…

Let $k$ be a field, and suppose that $\Gamma$ is a smooth $k$-group that acts on a connected, reductive $k$-group $\widetilde G$. Let $G$ denote the maximal smooth, connected subgroup of the group of $\Gamma$-fixed points in $\widetilde G$.…

A topological group G is said to be almost maximally almost-periodic if its von Neumann radical is non-trivial, but finite. In this paper, we prove that every abelian group with an infinite torsion subgroup admits a (Hausdorff) almost…

We introduce invertible subalgebras of local operator algebras on lattices. An invertible subalgebra is defined to be one such that every local operator can be locally expressed by elements of the inveritible subalgebra and those of the…

By classifying $S$-maximal amenable subgroups of algebraic groups over a global field of characteristic zero, we obtain a complete classification of maximal amenable subgroups up to commensurability in the respective arithmetic groups.…

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 a countably infinite group $\Gamma$, let $\mathcal{W}_\Gamma$ denote the space of all weak equivalence classes of measure-preserving actions of $\Gamma$ on atomless standard probability spaces, equipped with the compact metrizable…

We introduce the vertex-arboricity of group-labelled graphs. For an abelian group $\Gamma$, a $\Gamma$-labelled graph is a graph whose edges are labelled by elements of $\Gamma$. For an abelian group $\Gamma$ and $A\subseteq \Gamma$, the…

We show that if a group $G$ acts geometrically by type-preserving automorphisms on a building, then $G$ satisfies the weak Tits alternative, namely, that $G$ is either virtually abelian or contains a non-abelian free group.

In this paper we describe all group gradings by a finite abelian group $\Gamma$ of a simple Lie algebra of type $G_2$ over an algebraically closed field $F$ of characteristic 0.

We present the most general gauge-invariant action functional for coupled 1- and 2-form gauge fields with kinetic terms in generic dimensions, i.e. dropping eventual contributions that can be added in particular space-time dimensions only…

Let $\Gamma$ be a countable group and $(X, \Gamma)$ a compact topological dynamical system. We study the question of the existence of an intermediate $C^*$-subalgebra $\mathcal{A}$ $$C^{*}_{r}(\Gamma)<\mathcal{A}<C(X)\rtimes_r\Gamma,$$…

We construct free abelian subgroups of the group $U(A_\Gamma)$ of untwisted outer automorphisms of a right-angled Artin group, thus giving lower bounds on the virtual cohomological dimension. The group $U(A_\Gamma)$ was previously studied…

This paper investigates the structure of $K_2$-groups for certain quotient rings of the integral group ring $\mathbb{Z}[G]$. Let $G$ be a finite abelian $p$-group with $p$-rank $r$, let $\Gamma$ be the maximal $\mathbb{Z}$-order of…

As an analogue of the topological boundary of discrete groups $\Gamma$, we define the noncommutative topological boundary of tracial von Neumann algebras $(M, \tau)$ and apply it to generalize the main results of [AHO23], showing that for a…

For a maximal abelian subalgebra $A\subset M$ in a finite von Neumann algebra, we consider an invariant due to Takesaki which is an equivalence relation on a standard probability space. We give several characterization of this invariant and…