5 papers · 1 filter
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…