Related papers: Non-commutative Intermediate Factor theorem associ…

We prove that any tensor product factorization with a commutative factor of a modular group algebra over a prime field comes from a direct product decomposition of the group basis. This extends previous work by Carlson and Kov\'acs for the…

Let $I$ be any nonempty set and $(M_i, \varphi_i)_{i \in I}$ any family of nonamenable factors, endowed with arbitrary faithful normal states, that belong to a large class $\mathcal C_{\rm anti-free}$ of (possibly type III) von Neumann…

For an action $\alpha$ of a locally compact group $G$ on a dual operator space $X$ by w*-continuous completely isometric isomorphisms one can define two generally different notions of crossed products, namely the Fubini crossed product…

For $\MvN$ a separable, purely infinite von Neumann algebra with almost periodic weight $\phi$, a decomposition of $\MvN$ as a crossed product of a semifinite von Neumann algebra by a trace--scaling action of a countable abelian group is…

In the mid thirties Murray and von Neumann found a natural way to associate a von Neumann algebra $L(\Gamma)$ to any countable discrete group $\Gamma$. Classifying $L(\Gamma)$ in term of $\Gamma$ is a notoriously complex problem as in…

In the context of finite tensor products of Hilbert spaces, we prove that similarity of a tensor product of operator semigroups to a contraction semigroup is equivalent to the corresponding similarity for each factor, after an appropriate…

We prove that any weak* continuous semigroup $(T_t)_{t \geq 0}$ of factorizable Markov maps acting on a von Neumann algebra $M$ equipped with a normal faithful state can be dilated by a group of Markov $*$-automorphisms analogous to the…

We introduce a framework allowing for key aspects of deformation/rigidity theory to be used in the study of continuous model theory of II$_1$ factors. Using this framework, we solve several well-known open problems in the area. For example,…

Suppose $G$ is a free product $G = A_1 * A_2* \cdots * A_k * F_N$, where each of the groups $A_i$ is torsion-free and $F_N$ is a free group of rank $N$. Let $\mathcal{O}$ be the deformation space associated to this free product…

Let B be a C*-algebra with a maximal coaction of a locally compact group G, and let N and H be closed normal subgroups of G with N contained in H. We show that the process Ind_(G/H)^G which uses Mansfield's bimodule to induce…

We introduce a new algebraic framework to describe gravitational scrambling, including the semiclassical limit of any out-of-time-order correlation function that is built out of operator insertions separated by approximately the scrambling…

Let $\mathfrak F$ be a locally compact nonarchimedean field of positive residue characteristic $p$ and $k$ a field of characteristic $p$. Let $G$ be the group of $\mathfrak{F}$-rational points of a connected reductive group over…

We consider two von Neumann subalgebras $\cl B_0$ and $\cl B$ of a type ${\rm{II}}_1$ factor $\cl N$. For a map $\phi$ on $\cl N$, we define \[\|\phi \|_{\infty,2}=\sup\{\|\phi(x)\|_2\colon \|x\| \leq 1\},\] and we measure the distance…

We consider $\text{\rm II}_1$ factors $L_\mu(G)$ arising from 2-cocyles $\mu \in \text{\rm H}^2(G,\Bbb T)$ on groups $G$ containing infinite normal subgroups $H \subset G$ with the relative property $\text{\rm(T)}$ (i.e. $G$ {\it w-rigid}).…

Recall that a unitary in a tracial von Neumann algebra is Haar if $\tau(u^n)=0$ for all $n\in \mathbb{N}$. We introduce and study a new Borel equivalence relation $\sim_N$ on the set of Haar unitaries in a diffuse tracial von Neumann…

We consider amalgamated free product II$_1$ factors $M = M_1 *_B M_2 *_B ...$ and use ``deformation/rigidity'' and ``intertwining'' techniques to prove that any relatively rigid von Neumann subalgebra $Q\subset M$ can be intertwined into…

We consider II$_1$ factors of the form $M=\bar{\bigotimes}_{G}N\rtimes G$, where either i) $N$ is a non-hyperfinite II$_1$ factor and $G$ is an ICC amenable group or ii) $N$ is a weakly rigid II$_1$ factor and $G$ is ICC group and where $G$…

Practically and intrinsically, inclusions of operator algebras are of fundamental interest. The subject of this paper is intermediate operator algebras of inclusions. There are two previously known theorems which naturally and completely…

We define the notion of self-tracial stability for tracial von Neumann algebras and show that a tracial von Neumann algebra satisfying the Connes Embedding Problem is self-tracially stable if and only if it is amenable. We then generalize a…

We prove some unique prime factorization results for tensor products of type $II_1$ factors of the form $\Gamma_q(\mathbb{C}, S \otimes H)$ arising from symmetric independent copies with sub-exponential dimensions of the spaces $D_k(S)$ and…