Characters of solvable groups, Hilbert–Schmidt stability and dense periodic measures

Arie Levit*, Itamar Vigdorovich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study the character theory of metabelian and polycyclic groups. It is used to investigate Hilbert–Schmidt stability via the character-theoretic criterion of Hadwin and Shulman. There is a close connection between stability and dynamics of automorphisms of compact abelian groups. Relying on this, we deduce that finitely generated virtually nilpotent groups, free metabelian groups, lamplighter groups as well as upper triangular groups over certain rings of algebraic integers are Hilbert–Schmidt stable.

Original languageEnglish
JournalMathematische Annalen
DOIs
StateAccepted/In press - 2023

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