Related papers: Factoriality of q-Gaussian von Neumann algebras
The groups distinguish their von Neumann algebras, in the case when these are factors.
We study the von Neumann algebra generated by q--deformed Gaussian elements l_i+l_i^* where operators l_i fulfill the q--deformed canonical commutation relations l_i l_j^*-q l_j^* l_i=delta_{ij} for -1<q<1. We show that if the number of…
We establish factoriality of $q$-Araki-Woods von Neumann algebras (with the number of generators at least two) in full generality, exploiting the approach via conjugate variables developed recently in the tracial case by Akihiro Miyagawa…
It is proved that the $q$-Araki-Woods von Neumann algebras $\Gamma_q(\CH_\R,U_t)^{\prime\prime}$ for $q\in (-1,1)$ are factors if $dim(\CH_\R)\geq 3$.
For any given integer $n\geq 1$, we construct i.c.c. groups $G$ such that the II$_1$ factors $L(G)$ have exactly $n$-many $G$-invariant von Neumann subalgebras not arising from subgroups.
The Hecke algebra $\mathbb{C}_q[W]$ of a Coxter group $W$, associated to parameter $q$, can be completed to a von Neumann algebra $\mathcal{N}_q(W)$. We study such algebras in case where $W$ is right-angled. We determine the range of $q$…
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…
We study the $t$-deformation of gaussian von Neumann algebras. They appear as example in the theories of Interacting Fock spaces and conditionally free products. When the number of generators is fixed, it is proved that if $t$ sufficiently…
We study the von Neumann algebra, generated by the unitary representations of infinite-dimensional groups nilpotent group $B_0^{\mathbb N}$. The conditions of the irreducibility of the regular and quasiregular representations of…
This is a continuation of our previous paper studying the structure of Cartan subalgebras of von Neumann factors of type II_1. We provide more examples of II_1 factors having either zero, one or several Cartan subalgebras. We also prove a…
In the paper, we study the generator problem of II$_1$ factors. By defining a new concept related to the number of generators of a von Neumann algebra, we are able to show that a large class of II$_1$ factors are singly generated, i.e.,…
We quantize JT gravity with matter on the spatial interval with two asymptotically AdS boundaries. We consider the von Neumann algebra generated by the right Hamiltonian and the gravitationally dressed matter operators on the right…
We prove a basic result about tensor products of a $\text{II}_1$ factor with a finite von Neumann algebra and use it to answer, affirmatively, a question asked by S. Popa about maximal injective factors.
These notes provide an explanation of the type classification of von Neumann algebras, which has made many appearances in recent work on entanglement in quantum field theory and quantum gravity. The goal is to bridge a gap in the literature…
This work addresses a full characterization of three new q-polynomials derived from the $q-$oscillator algebra. Related matrix elements and generating functions are deduced. Further, a connection between Hahn factorial and q-Gaussian…
The $q$-deformed Araki-Woods von Neumann algebras $\Gamma_q(\mathcal{H}_\mathbb{R}, U_t)^{\prime \prime}$ are factors for all $q\in (-1,1)$ whenever $dim(\mathcal{H}_\mathbb{R})\geq 3$. When $dim(\mathcal{H}_\mathbb{R})=2$ they are factors…
We give a characterisation of factoriality of the groupoid von Neumann algebra $L(\mathcal{G})$ associated to a discrete measured groupoid $(\mathcal{G},\mu)$. We introduce the notion of groupoids with `infinite conjugacy classes' and show…
In this article, we give explicit examples of maximal amenable subalgebras of the $q$-Gaussian algebras, namely, the generator subalgebra is maximal amenable inside the $q$-Gaussian algebras for real numbers $q$ with its absolute value…
We give some natural conditions on actions of discrete countable groups on abelian locally compact groups of Lie type that imply factoriality of the group von Neumann algebras of their semidirect products. This allows us to give a fairly…
This paper includes a series of structural results for von Neumann algebras arising from measure preserving actions by product groups on probability spaces. Expanding upon the methods used earlier by the first two authors \cite{CS}, we…