Related papers: Examples of compact quantum groups with $\operator…

A subfactor is an inclusion $N \subset M$ of von Neumann algebras with trivial centers. The simplest example comes from the fixed points of a group action $M^G \subset M$, and subfactors can be thought of as fixed points of more general…

Developing new techniques at the interface of geometric group theory and von Neumann algebras, we identify the first examples of ICC groups $G$ whose von Neumann algebras are McDuff and exhibit a new rigidity phenomenon, termed McDuff…

A variant of Gromov's notion of measure equivalence for groups has been introduced for II$_1$ factors under different names. We propose the terminology of W*-correlated II$_1$ factors. We prove rigidity results up to W*-correlations for…

For every uncountable cardinal $\kappa$ there are $2^\kappa$ nonisomorphic simple AF algebras of density character $\kappa$ and $2^\kappa$ nonisomorphic hyperfinite II$_1$ factors of density character $\kappa$. These estimates are maximal…

In this paper, we study the quantum channel on a von Neuamnn algebra $\mathcal{M}$ preserving a von Neumann subalgebra $\mathcal{N}$, namely an $\mathcal{N}$-$\mathcal{N}$-bimodule unital completely positive map. By introducing the relative…

In the given article it is introduced new notions of a C$^*$-algebra of von Neumann type I and C$^*$-algebras of types I$_n$, II, II$_1$, II$_\infty$ and III. It is proved that any GCR-algebra is a C$^*$-algebra of von Neumann type I, and a…

This paper is the third of a series giving a self-contained way from the Neveu-Schwarz algebra to a new series of irreducible subfactors. Here we introduce the local von Neumann algebra of the Neveu-Schwarz algebra, to obtain…

The first part of this paper is a refinement of Winkelmann's work on invariant rings and quotients of algebraic groups actions on affine varieties, where we take a more geometric point of view. We show that the (algebraic) quotient…

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…

In this paper we introduce a new class of non-amenable groups denoted by ${\bf NC}_1 \cap {\bf Quot}(\mathcal C_{rss})$ which give rise to $\textit{prime}$ von Neumann algebras. This means that for every $\Gamma \in {\bf NC}_1 \cap {\bf…

Let $K$ be an arbitrary field of characteristic zero and $A$ a commutative associative $ K$-algebra which is an integral domain. Denote by $R$ the fraction field of $A$ and by $W(A)=RDer_{\mathbb K}A,$ the Lie algebra of $\mathbb…

Let $G$ be a countable discrete amenable group, ${\cal M}$ a McDuff factor von Neumann algebra, and $A$ a separable nuclear weakly dense C$^*$-subalgebra of ${\cal M}$. We show that if two centrally free actions of $G$ on ${\cal M}$ differ…

Let $G = G_{1} \times G_{2}$ be a product of two locally compact, second countable groups and $\mu \in \mathrm{Prob}(G)$ be of the form $\mu = \mu_{1} \times \mu_{2}$, where $\mu_{i} \in \mathrm{Prob}(G_{i})$. Let $(B,\nu_B)$ be the…

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…

We approach the study of sub-von Neumann algebras of the group von Neumann algebra $L\Gamma$ for countable groups $\Gamma$ from a dynamical perspective. It is shown that $L(\Gamma)$ admits a maximal invariant amenable subalgebra. The notion…

For a locally compact group G and a compact subgroup K, the corresponding Hecke algebra consists of all continuous compactly supported complex functions on G that are K-bi-invariant. There are many examples of totally disconnected locally…

Let M be a von Neumann algebra of type II_1 which is also a complemented subspace of B(H). We establish an algebraic criterion, which ensures that M is an injective von Neumann algebra. As a corollary we show that if M is a complemented…

We construct the first examples of purely continuous, $q$-deformed Lie type locally compact quantum groups in higher rank. They arise from Drinfeld-Jimbo quantization, at unimodular deformation parameter, of the totally positive part of…

A manifestly Lorentz-covariant formulation of Loop Quantum Gravity (LQG) is given in terms of finite-dimensional representations of the Lorentz group. The formulation accounts for discrete symmetries, such as parity and time-reversal, and…

We show that for F an invertible 2 by 2 matrix, the von Neumann algebra associated to the universal quantum group A_u(F) is a free Araki-Woods factor.