Related papers: There is no separable universal II_1-factor

The problem of the existence of non-pseudo-$\aleph_1$-compact $\mathbb R$-factorizable groups is studied. It is proved that any such group is submetrizable and has weight larger than $\omega_1$. Closely related results concerning the…

We prove that if a sequence of geodesically complete CAT$(0)$-spaces $X_j$ with uniformly cocompact discrete groups of isometries converges in the Gromov-Hausdorff sense to $X_\infty$, then the dimension of the maximal Euclidean factor…

We consider three notions of divisibility in the Cuntz semigroup of a C*-algebra, and show how they reflect properties of the C*-algebra. We develop methods to construct (simple and non-simple) C*-algebras with specific divisibility…

We study generic properties of topological groups in the sense of Baire category. First we investigate countably infinite (discrete) groups. We extend a classical result of B. H. Neumann, H. Simmons and A. Macintyre on algebraically closed…

It is well known there is no finitely generated abelian group which has the $R_\infty$ property. We will show that also many non-finitely generated abelian groups do not have the $R_\infty$ property, but this does not hold for all of them.…

No type II$_1$ tracial von Neumann algebra has theory that admits quantifier elimination.

For any (unital) exchange ring $R$ whose finitely generated projective modules satisfy the separative cancellation property ($A\oplus A\cong A\oplus B\cong B\oplus B$ implies $A\cong B$), it is shown that all invertible square matrices over…

We generalize the main result of Kamalov and show that if $G$ is an amenable discrete group with an action $\alpha$ on a finite nuclear unital $C^*$-algebra $A$ such that the reduced crossed product $A\rtimes_{\alpha,r} G$ has property $T$,…

The construction of a C*-algebra of a differential groupoid is presented. It is shown that it defines a covariant functor from the category of differential groupoids in a sense of S. Zakrzewski to the category of C*-algebras.

A version of Gromov's cup product lemma in which one factor is the (1,0)-part of the differential of a continuous plurisubharmonic function is obtained. As an application, it is shown that a connected noncompact complete Kaehler manifold…

Notions of higher Kazhdan property can be defined in terms of vanishing of unitary group cohomology in higher degrees. Garland's theorem for simple groups over non-archimedean fields provides the first examples of a higher Kazhdan property.…

We show that it is consistent with ZFC that there is a simple nuclear non-separable C*-algebra which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the…

Let a compact group G act on real or complex C*-algebras A and B, with A separable and B sigma-unital. We express the G-equivariant Kasparov groups KK_n(A,B) by algebraic K-groups of a certain additive category.

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.,…

We prove unit-free versions of both the associative and the non-associative Vidav-Palmer theorems. Then these results are applied to prove a unit-free version of the Blecher-Ruan-Sinclair non-associative characterization of unital…

The property that the polynomial cohomology with coefficients of a finitely generated discrete group is canonically isomorphic to the group cohomology is called the (weak) isocohomological property for the group. In the case when a group is…

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 machine developed by the second author produces a rich family of unitary representations of the Thompson groups F,T and V. We use it to give direct proofs of two previously known results. First, we exhibit a unitary representation of V…

We say that a C*-algebra X has the approximate n-th root property (n\geq 2) if for every a\in X with ||a||\leq 1 and every \epsilon>0 there exits b\in X such that ||b||\leq 1 and ||a-b^n||<\epsilon. Some properties of commutative and…

We prove that every rigid C*-bicategory with finite-dimensional centers (finitely decomposable horizontal units) can be realized as Connes' bimodules over finite direct sums of II$_1$ factors. In particular, we realize every multitensor…