Related papers: Operator-algebraic superrigidity for $SL_n(\mathbb…

For $p\in [1,\infty)$, we show that every unital $L^p$-operator algebra contains a unique maximal $C^*$-subalgebra, which is always abelian if $p\neq 2$. Using this, we canonically associate to every unital $L^p$-operator algebra $A$ an…

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 study from an algebraic point of view the question of extending an action of a group \(\Gamma\) on a commutative domain \(R\) to a formal pseudodifferential operator ring \(B=R(\!(x\,;\,d)\!)\) with coefficients in \(R\), as well as to…

A unital $C^*$-algebra is called $N$-subhomogeneous if its irreducible representations are finite dimensional with dimension at most $N$. We extend this notion to operator systems, replacing irreducible representations by boundary…

Consider a free ergodic measure preserving profinite action $\Gamma\curvearrowright X$ (i.e. an inverse limit of actions $\Gamma\curvearrowright X_n$, with $X_n$ finite) of a countable property (T) group $\Gamma$ (more generally of a group…

Let $\Gamma$ be a countable discrete group. We say that $\Gamma$ has $C^*$-invariant subalgebra rigidity (ISR) property if every $\Gamma$-invariant $C^*$-subalgebra $\mathcal{A}\le C_r^*(\Gamma)$ is of the form $C_r^*(N)$ for some normal…

Let $A$ be a separable (not necessarily unital) simple $C^*$-algebra with strict comparison. We show that if $A$ has tracial approximate oscillation zero then $A$ has stable rank one and the canonical map $\Gamma$ from the Cuntz semigroup…

We study the uniform property $\Gamma$ for separable simple $C^*$-algebras which have quasitraces and may not be exact. We show that a stably finite separable simple $C^*$-algebra $A$ with strict comparison and uniform property $\Gamma$ has…

We consider the tracial crossed product algebra $M=A\rtimes\Lambda$ arising from a trace preserving action $\sigma:\Lambda \curvearrowright A$ of a discrete group $\Lambda$ on a tracial von Neumann algebra $A$. For a unitary subgroup…

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…

Using an interplay between geometric methods in group theory and soft von Neuman algebraic techniques we prove that for any icc, acylindrically hyperbolic group $\Gamma$ its von Neumann algebra $L(\Gamma)$ satisfies the so-called ISR…

To each complex reflection group $\Gamma$ one can attach a canonical symplectic singularity $\mathcal{M}_\Gamma$ arXiv:math/9903070. Motivated by the 4D/2D duality arXiv:1312.5344, arXiv:1707.07679, Bonetti, Meneghelli and Rastelli…

Let $\Gamma$ be a weakly irreducible higher rank lattice. In this paper, we will prove various rigidity results for the $\Gamma$-action following a philosophy of the Zimmer program. We provide new rigidity results including local and global…

We study Cartan subalgebras in the context of amalgamated free product II$_1$ factors and obtain several uniqueness and non-existence results. We prove that if $\Gamma$ belongs to a large class of amalgamated free product groups (which…

We prove that separable, simple, unital, non-elementary, stably finite C*-algebras that have stable rank one, and that have locally finite nuclear dimension in a tracial sense, have uniform property $\Gamma$. In particular, Villadsen…

We demonstrate von Neumann algebra arising from an icc group $\Gamma$ in Chifan's, Ioana's, and Kida's class of poly-$\mathcal{C}_\text{rss} $, such as a poly-hyperbolic group with no amenable factors in its composition series, satisfies…

A conjecture of Kadison and Kastler from 1972 asks whether sufficiently close operator algebras in a natural uniform sense must be small unitary perturbations of one another. For $n\geq 3$ and a free ergodic probability measure preserving…

This note describes a unified approach to several superrigidity results, old and new, concerning representations of lattices into simple algebraic groups over local fields. For an arbitrary group $\Gamma$ and a $\Gamma$-boundary $B$ we…

Let $\Gamma$ be a $T$-ideal of identities of an affine PI-algebra over an algebraically closed field $F$ of characteristic zero. Consider the family $\mathcal{M}_{\Gamma}$ of finite dimensional algebras $\Sigma$ with $Id(\Sigma) = \Gamma$.…

Let M be a factor of type III with separable predual and with normal states phi_1,...,phi_k, omega with omega faithful. Let A be a finite dimensional C*-subalgebra of M. Then it is shown that there is a unitary operator u in M such that…