Related papers: Two applications of free entropy

We prove that the first order theory of nonabelian free groups eliminates the "there exists infinitely many" quantifier (in eq). Equivalently, since the theory of nonabelian free groups is stable, it does not have the finite cover property.…

We prove that the first continuous $L^2$-cohomology of free group factors vanishes. This answers a question by Andreas Thom regarding continuity properties of free difference quotients and shows that one can not distinguish free group…

We compare finiteness properties of locally compact groups that generalize the properties of being compactly generated and of being compactly presented. Three such families of properties have been proposed: Abels--Tiemeyer's type $C_n$,…

We prove that if $A$ is a non-separable abelian tracial von Neuman algebra then its free powers $A^{*n}, 2\leq n \leq \infty$, are mutually non-isomorphic and with trivial fundamental group, $\mathcal F(A^{*n})=1$, whenever $2\leq…

Given a subfactor planar algebra P, Guionnet, Jones and Shlyakhtenko give a diagrammatic construction of a II_{1} subfactor whose planar algebra is P. They showed if P is finite-depth, then the factors are interpolated free group factors,…

We study the algebraic entropy of continuous endomorphisms of compactly covered, locally compact, topologically quasihamiltonian groups. We provide a Limit-free formula which helps us to simplify the computations of this entropy. Moreover,…

The aim of this manuscript is to study some local properties of the topological entropy of a free semigroup action. In order to do that we focus on the set of entropy points of a free semigroup action, show that this set carries the full…

We study the relation between the structure of algebraic and context-free subsets of a group G and that of a finite index subgroup H. Using these results, we prove that a kind of Fatou property, previously studied by Berstel and Sakarovitch…

This talk is organized as follows: First we explain some basic concepts in non-commutative probability theory in the frame of operator algebras. In Section 2, we discuss related topics in von Neumann algebras. Sections 3 and 4 contain some…

We provide a unifying approach which links results on algebraic actions by Lind and Schmidt, Chung and Li, and a topological result by Meyerovitch that relates entropy to the set of asymptotic pairs. In order to do this we introduce a…

We prove that if $A_1, A_2, \dots, A_n$ are tracial abelian von Neumann algebras for $2\leq n \leq \infty$ and $M = A_1 * \cdots * A_n$ is their free product, then any subalgebra $A \subset M$ of the form $A = \sum_{i=1}^n u_i A_i p_i…

We show that if $G$ is a non-archimedean, Roelcke precompact, Polish group, then $G$ has Kazhdan's property (T). Moreover, if $G$ has a smallest open subgroup of finite index, then $G$ has a finite Kazhdan set. Examples of such $G$ include…

Realizing free semicircular elements on the full Fock space, we prove an equivalence between rationality of operators obtained from them and finiteness of the rank of their commutators with right annihilation operators. This is an analogue…

We prove that the reduced group C*-algebras of infinite countable discrete groups having topologically-free extreme boundaries, or more generally groups that satisfy certain combinatorial property including all acylindrically hyperbolic…

We begin a study of a pro-$p$ analogue of limit groups via extensions of centralizers and call $\mathcal{L}$ this new class of pro-$p$ groups. We show that the pro-$p$ groups of $\mathcal{L}$ have finite cohomological dimension, type…

Let $F$ be either a free nilpotent group of a given class and of finite rank or a free solvable group of a certain derived length and of finite rank. We show precisely which ones have the $R_{\infty}$ property. Finally, we also show that…

We prove that for any free ergodic probability measure preserving action \F_n \actson (X,\mu) of a free group on n generators \F_n, 2 \leq n \leq \infty, the associated group measure space II_1 factor $L^\infty(X) \rtimes \F_n$ has…

Let W be an affine PI algebra over a field of characteristic zero graded by a finite group G. We show that there exist $\alpha_{1},\alpha_{2}\in\mathbb{R}, \beta\in\frac{1}{2}\mathbb{Z}$, and $l\in\mathbb{N}$ such that…

We continue previous work on Voiculescu's topological free entropy dimension {\delta}_{top}. We introduce the notions of MF-trace, MF-ideal, and MF-nuclearity and use these concepts to obtain upper and lower bounds for {\delta}_{top}, and…

Let $M_n$ be a sequence of finite factors with $\dim(M_n)\rightarrow \infty$ and denote $\text{\bf M}=\Pi_\omega M_n$ their ultraproduct over a free ultrafilter $\omega$. We prove that if $\text{\bf Q}\subset \text{\bf M}$ is either an…