11 papers
Spectral gap, internality of relative commutants, and non-hyperlinear groups
Vadim Alekseev, Jihao Liu, Andreas Thom
We prove that the relative commutant of a finite unitary tuple in a tracial matrix ultraproduct is internal whenever its conjugation operator has a spectral gap off the commutant.…
Images of word maps with constants on algebraic groups
Vadim Alekseev, Jakob Schneider
We study word maps with constants on quasisimple algebraic groups over a local field . We prove that, for such a group and a word $w\in (G\ast\mathbf{F}_r)\set…
Centralizers of sofic approximations of Kazhdan groups
Vadim Alekseev, Andreas Thom
We prove that a Kazhdan group admitting a sofic embedding into a metric ultraproduct of symmetric groups with a centralizer that acts ergodically on the associated Loeb probability…
The hyperfinite II-factor is Ulam stable
Vadim Alekseev, Andreas Thom
We prove Ulam stability of the hyperfinite II-factor with respect to the trace norm on the operator-norm unit ball. More precisely, every sufficiently additive, multiplicative,…
Sofic actions, halo products, and metric approximations of groups
Vadim Alekseev, Henry Bradford
We introduce the notion of a ``sofic -action'' of one group on another by automorphisms, for a class of groups. We show that if is the clas…
Remarks on approximability and stability for groups
Vadim Alekseev, Andreas Thom
In this paper, we provide several instances in which interesting approximation and stability properties are inherited by quotients with respect to finitely generated normal subgrou…
On finite local approximations of isometric actions of residually finite groups
Vadim Alekseev, Andreas Thom
We show that any isometric action of a residually finite group admits approximate local finite models. As a consequence, if is residually finite, every isometric -action emb…
On the asymptotic equidistribution of word values in symmetric groups
Vadim Alekseev, Jakob Schneider, Andreas Thom
We prove an asymptotic equidistribution result for word values for words with constants in the symmetric group. We also speculate about simultaneous asymptotic equidistribution res…
Amenability and skew-amenability of actions of topological groups
Vadim Alekseev, Hiroshi Ando, Friedrich Martin Schneider +1
We define and study notions of amenability and skew-amenability of continuous actions of topological groups on compact topological spaces. Our main motivation is the question under…
On non-isomorphic universal sofic groups
Vadim Alekseev, Andreas Thom
We show that there are non-isomorphic universal sofic groups. This proves a conjecture of Simon Thomas.
About discrete subgroups of full groups of measure preserving equivalence relations
Vadim Alekseev, Alessandro Carderi, Andreas Thom +1
In this note we study countable subgroups of the full group of a measure preserving equivalence relation. We provide various constraints on the group structure, the nature of the a…