4 papers · 2 filters
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.…
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…
On the Howe--Moore property for automorphism groups of buildings
Pierre-Emmanuel Caprace, Andreas Thom
Let be a closed type-preserving subgroup of the automorphism group of a thick locally finite building of finite rank, and assume that acts Weyl-transitively. We prove t…
Cubic maps from the group of order
Vadim Alekseev, Andreas Thom
The purpose of this note is to classify unital cubic maps from the cyclic group of order into an arbitrary non-abelian group. We show that the universal group admitting a unita…