Related papers: W*-superrigidity for groups with infinite center

Let $M$ be a finite von Neumann algebra. In the first part, we give asymptotic results about $M$-stable sequences of weak*-continuous mappings which are related with operators belonging to $M$. In the second part, we extend, by a shorter…

For any $n\geqslant 4$ let $\tilde B_n=B_n/Z(B_n)$ be the quotient of the braid group $B_n$ through its center. We prove that any free ergodic probability measure preserving (pmp) action $\tilde B_n\curvearrowright (X,\mu)$ is…

We introduce certain $C^*$-algebras and $k$-graphs associated to $k$ finite dimensional unitary representations $\rho_1,...,\rho_k$ of a compact group $G$. We define a higher rank Doplicher-Roberts algebra $\mathcal{O}_{\rho_1,...,\rho_k}$,…

This work discovers a novel link between probability theory (of stable random fields) and von Neumann algebras. It is established that the group measure space construction corresponding to a minimal representation is an invariant of a…

We prove a super-rigidity result for algebraic representations over complete fields of irreducible lattices in product of groups and lattices with dense commensurator groups. We derive some criteria for non-linearity of such groups.

We give a definition of differentiable cohomology of a Lie group G (possibly infinite-dimensional) with coefficients in any abelian Lie group. This differentiable cohomology maps both to the cohomology of the group made discrete and to Lie…

Let $A$ be a $C^*$-algebra. We say that $A$ satisfies the SP if every bounded homomorphism $A\to B(K)$, with $K$ a Hilbert space, is similar to a $*$-homomorphism. We introduce three hypotheses that relate to extending hyperreflexive…

We consider converses to the density theorem for irreducible, projective, unitary group representations restricted to lattices using the dimension theory of Hilbert modules over twisted group von Neumann algebras. We show that under the…

Chung and Jiang showed that, if a one ended group contains an infinite order element, then every continuous cocycle over the full shift on that group, taking values in a discrete group, must be cohomologous to a homomorphism. We show that…

The goal of the paper is to introduce a version of Schubert calculus for each dihedral reflection group W. That is, to each "sufficiently rich'' spherical building Y of type W we associate a certain cohomology theory and verify that, first,…

We show that the nuclear dimension of a (twisted) group C*-algebra of a virtually polycyclic group is finite. This prompts us to make a conjecture relating finite nuclear dimension of group C*-algebras and finite Hirsch length, which we…

Motivated by Popa's seminal work \cite{Po04}, in this paper, we provide a fairly large class of examples of group actions $\Gamma \curvearrowright X$ satisfying the extended Neshveyev-St{\o}rmer rigidity phenomenon \cite{NS03}: whenever…

Let $(\mathcal{G},\nu)$ be a $t$-discrete ergodic groupoid. Consider a finite Von Neumann algebra $\mathcal{M}$ with separable predual. We prove that every uniformly bounded measurable representation $\rho:\mathcal{G} \rightarrow…

Let Wh^w(G) be the K_1-group of square matrices over the integral group ring ZG which are not necessarily invertible but induce weak isomorphisms after passing to Hilbert space completions. Let D(G) be the division closure of ZG in the…

We show that C*-algebras generated by irreducible representations of finitely generated nilpotent groups satisfy the universal coefficient theorem of Rosenberg and Schochet. This result combines with previous work to show that these…

The Lodha-Moore group $G$ first arose as a finitely presented counterexample to von Neumann's conjecture. The group $G$ acts on the unit interval via piecewise projective homemorphisms. A result of Lodha shows that $G$ in fact has type…

We analyse the global symmetry structure of two-dimensional Non-Linear Sigma Models with Wess-Zumino term. When the target space has a compact isometry without fixed points, the theory has a pair of (group-like) global symmetries and many…

We unify the Kumjian-Renault Weyl groupoid construction with the Lawson-Lenz version of Exel's tight groupoid construction. We do this by utilising only a weak algebraic fragment of the C*-algebra structure, namely its *-semigroup reduct.…

We show that any connected algebraic group $G$ over a field admits a nilpotent normal subgroup $Z_\infty(G)$ such that the quotient $G/Z_\infty(G)$ has trivial center. We construct $Z_\infty(G)$ as the final term of the transfinitely…

We systematically investigate cocycle superrigidity in the setting of finite rank median spaces for product groups and Kazhdan groups. By employing a dynamical approach to superrigidity, we establish, for a median space X of finite rank,…