相关论文: Tight decomposition of factors and the single gene…

We examine the notion of $\alpha$-strong singularity for subfactors of a \IIi factor, which is a metric quantity that relates the distance between a unitary in the factor and a subalgebra with the distance between that subalgebra and its…

Let a and b be non-zero rational numbers that are multiplicatively independent. We study the natural density of the set of primes p for which the subgroup of the multiplicative group of the finite field with p elements generated by (a\mod…

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.

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…

Let $\mathfrak{g}$ be a simple complex Lie algebra and let $\mathfrak{t} \subset \mathfrak{g}$ be a toral subalgebra of $\mathfrak{g}$. As a $\mathfrak{t}$-module $\mathfrak{g}$ decomposes as \[\mathfrak{g} = \mathfrak{s} \oplus…

Let $\M$ be a von Neumann algebra acting on a Hilbert space $\H$, and $\N$ be a singular von Neumann subalgebra of $\M.$ If $\N\tensor\B(\K)$ is singular in $\M\tensor\B(\K)$ for any Hilbert space $\K$, we say $\N$ is \emph{completely…

We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group $\SL_2$, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands.…

The structure of a certain subgroup $S$ of the automorphism group of a partially commutative group (RAAG) $G$ is described in detail: namely the subgroup generated by inversions and elementary transvections. We define admissible subsets of…

Let \( A \subset M \) be an inclusion of von Neumann algebras equipped with a faithful normal semifinite operator valued weight \( E \colon M \to A \). We prove that every positive element \( x \in M \) with \( E(x) < \infty \) satisfies…

We obtain several rigidity results regarding tensor product decompositions of factors. First, we show that any full factor with separable predual has at most countably many tensor product decompositions up to stable unitary conjugacy. We…

We show that graph products of non trivial finite dimensional von Neumann algebras are strongly 1-bounded when the underlying *-algebra has vanishing first L2-Betti number. The proof uses a combination of the following two key ideas to…

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…

In these notes we develop a link between the Kadison-Singer problem and questions about certain dynamical systems. We conjecture that whether or not a given state has a unique extension is related to certain dynamical properties of the…

We prove that every separable tracial von Neumann algebra embeds into a II$_1$ factor with property (T) which can be taken to have trivial outer automorphism and fundamental groups. We also establish an analogous result for the trivial…

Let $\phi$ be a psh function on a bounded pseudoconvex open set $\Omega \subset \C^n$, and let ${\cal I}(\phi)$ be the associated multiplier ideal sheaf. Motivated by resolution of singularities issues, we establish an effective version of…

We provide a fairly large family of amalgamated free product groups $\Gamma=\Gamma_1\ast_{\Sigma}\Gamma_2$ whose amalgam structure can be completely recognized from their von Neumann algebras. Specifically, assume that $\Gamma_i$ is a…

In this paper we establish a rigidity property of holomorphic generators by using their local behavior at a boundary point $\tau$ of the open unit disk $\Delta$. Namely, if $f\in\mathrm{Hol}(\Delta,\mathbb{C})$ is the generator of a…

Let $\mathcal M$ be a separable factor. An operator $T$ in $\mathcal{M}$ is said to be irreducible in $\mathcal{M}$ if the von Neumann algebra $W^*(T)$ generated by $T$ is an irreducible subfactor of $\mathcal{M}$, i.e.,…

Given a locally compact second countable group $G$ with a 2-cocycle $\omega$, we show that the restriction of the twisted Plancherel weight $\varphi^\omega_G$ to the subalgebra generated by a closed subgroup $H$ in the twisted group von…

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…