Related papers: Strongly 1-bounded von Neumann algebras

Suppose $M$ is a tracial von Neumann algebra embeddable into $\mathcal R^{\omega}$ (the ultraproduct of the hyperfinite $II_1$-factor) and $X$ is an $n$-tuple of selfadjoint generators for $M$. Denote by $\Gamma(X;m,k,\gamma)$ the…

Let $n\geq 2$ and $G_n=\mathbb{Z}^n\rtimes SL_n(\mathbb{Z})$. We classify all $G_n$-invariant von Neumann subalgebras in $L(G_n)$. For $n=2$, this gives an alternative proof of the previous result of Jiang-Liu. For $n\geq 3$, this gives the…

We study a generalization of free Poisson random measure by replacing the intensity measure with a n.s.f. weight $\varphi$ on a von Neumann algebra $M$. We give an explicit construction of the free Poisson random weight using full Fock…

We analyze the anomaly constraints on 6D supergravity theories with a single abelian U(1) gauge factor. For theories with charges restricted to $q = \pm1, \pm2$ and no tensor multiplets, anomaly-free models match those models that can be…

An extended search for anomaly free matter coupled $N=(1,0)$ supergravity in six dimension is carried out by two different methods which we refer to as the graphical and rank methods. In the graphical method the anomaly free models are…

For a selfadjoint element x in a tracial von Neumann algebra and $\alpha = \delta_0(x)$ we compute bounds for $\mathbb H^{\alpha}(x),$ where $\mathbb H^{\alpha}(x)$ is the free Hausdorff $\alpha$-entropy of $x.$ The bounds are in terms of…

We prove that if $\{(M_j, \tau_j)\}_{j\in J}$ are tracial von Neumann algebras, $s_j \in M_j$ are selfadjoint semicircular elements and $t=(t_j)_j$ is a square summable $J$-tuple of real numbers with at least two non-zero entries, then the…

We prove that the relative commutant of a diffuse von Neumann subalgebra in a hyperbolic group von Neumann algebra is always injective. It follows that any non-injective subfactor in a hyperbolic group von Neumann algebra is non-Gamma and…

We consider absolutely free nonassociative algebras and, more generally, absolutely free algebras with (maybe infinitely) many multilinear operations. Such algebras are described in terms of labeled reduced planar rooted trees. This allows…

With a minor change made in the previous construction we observe that any reduced HNN extension is precisely a compressed algebra of a certain reduced amalgamated free product in both the von Neumann algebra and the $C^*$-algebra settings.…

We survey some of the progress made recently in the classification of von Neumann algebras arising from countable groups and their measure preserving actions on probability spaces. We emphasize results which provide classes of…

We investigate the asymptotic structure of (possibly type III) crossed product von Neumann algebras $M = B \rtimes \Gamma$ arising from arbitrary actions $\Gamma \curvearrowright B$ of bi-exact discrete groups (e.g. free groups) on amenable…

Motivated by Popa's seminal work \cite{Po04}, in this paper, we provide a fairly large class of examples of group actions $\Gamma \curvearrowright X$ satisfying the extended Neshveyev-St{\o}rmer rigidity phenomenon \cite{NS03}: whenever…

We undertake a comprehensive study of structural properties of graph products of von Neumann algebras equipped with faithful, normal states, as well as properties of the graph products relative to subalgebras coming from induced subgraphs.…

We construct a class of II_1 factors M that admit unclassifiably many Cartan subalgebras in the sense that the equivalence relation of being conjugate by an automorphism of M is complete analytic, in particular non Borel. We also construct…

A free semigroupoid algebra is the closure of the algebra generated by a TCK family of a graph in the weak operator topology. We obtain a structure theory for these algebras analogous to that of free semigroup algebra. We clarify the role…

We study the von Neumann algebra, generated by the regular representations of the infinite-dimensional nilpotent group $B_0^{\mathbb Z}$. In [14] a condition have been found on the measure for the right von Neumann algebra to be the…

In this paper we introduce and study strongly singular maximal abelian self-adjoint subalgebras of type $II_1$ factors. We show that certain elements of free groups and of non-elementary hyperbolic groups generate such masas, and these also…

We establish the MF property of the reduced group $ C^* $-algebra of an amalgamated free product of countable Abelian discrete groups. This result is then used to give a characterization of the amalgamated free products of Abelian groups…

The main result concerns a sigma-unital C*-algebra A, a strongly lower semicontinuous element h of A**, the enveloping von Neumann algebra, and the set of self-adjoint elements a of A such that a \le h - delta 1 for some delta > 0, where 1…