Related papers: Quantifier elimination in II$_1$ factors

This paper has been withdrawn by the author. The conjecture follows from the finiteness of group von Neumann algebras.

We investigate Cartan subalgebras in nontracial amalgamated free product von Neumann algebras $M_1 \ast_B M_2$ over an amenable von Neumann subalgebra $B$. First, we settle the problem of the absence of Cartan subalgebra in arbitrary free…

Several techniques together with some partial answers are given to the questions of factoriality, type classification and fullness for amalgamated free product von Neumann algebras.

In 1985, van den Dries showed that the theory of the reals with a predicate for the integer powers of two admits quantifier elimination in an expanded language, and is hence decidable. He gave a model-theoretic argument, which provides no…

We show that neither the class of C*-algebras with Kirchberg's QWEP property nor the class of W*-probability spaces with the QWEP property are effectively axiomatizable (in the appropriate languages). The latter result follows from a more…

We prove that the von Neumann algebras generated by $n$ $q$-Gaussian elements, are factors for $n\ge 2$.

We introduce notation Q(1) * ... * Q(n) * L(F_r)$ for von Neumann algebra II_1 factors where $r$ is allowed to be negative. This notation is defined by rescalings of free products of II_1 factors, and is proved to be consistent with known…

We construct inner amenable groups G with infinite conjugacy classes and such that the associated II_1 factor does not have property Gamma of Murray and von Neumann. This solves a problem posed by Effros in 1975.

In this paper, Property $\Gamma$ for a type II$_{1}$ von Neumann algebra is introduced as a generalization of Murray and von Neumann's Property $\Gamma$ for a type II$_{1}$ factor. The main result of this paper is that if a type II$_{1}$…

Quantifier-elimination or model-completeness of the affine part of some classical first order theories are proved.

We exhibit a theory where definable types lack the amalgamation property.

For II$_1$ factors, we show that property (T) is equivalent to weak spectral gap in any inclusion into a larger tracial von Neumann algebra. We also show that not having non-zero almost central vectors in weakly mixing bimodules…

A reduction formula for compressions of von Neumann algebras arising as free products is proved. This shows that the fundamental group is all of the positive reals for some such algebras. Additionally, by taking a sort of free product with…

We introduce the notion of L^2-rigidity for von Neumann algebras, a generalization of property (T) which can be viewed as an analogue for the vanishing of 1-cohomology into the left regular representation of a group. We show that…

We consider categorical logic on the category of Hilbert spaces. More generally, in fact, any pre-Hilbert category suffices. We characterise closed subobjects, and prove that they form orthomodular lattices. This shows that quantum logic is…

We show that the first order structure whose underlying universe is $\mathbb C$ and whose basic relations are all algebraic subset of $\mathbb C^2$ does not have quantifier elimination. Since an algebraic subset of $\mathbb C ^2$ needs…

Richard Kadison showed that not every commutative von Neumann subalgebra of a factor von Neumann algebra is equal to its relative double commutant. We prove that every commutative C*-subalgebra of a centrally prime C*-algebra $B$ equals its…

Let $A$ be a von Neumann algebra with no central summands of type $I_1$. We will show that every nonlinear Lie $n$-derivation on $A$ is of the standard form, i.e. it can be expressed as a sum of an additive derivation and a central-valued…

We show that when $M,N_{1},N_{2}$ are tracial von Neumann algebras with $M'\cap M^{\omega}$ abelian, $M'\cap(M\bar{\otimes}N_{1})^{\omega}$ and $M'\cap(M\bar{\otimes}N_{2})^{\omega}$ commute in…

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…