TY - JOUR
T1 - Characters of solvable groups, Hilbert–Schmidt stability and dense periodic measures
AU - Levit, Arie
AU - Vigdorovich, Itamar
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023.
PY - 2024/7
Y1 - 2024/7
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85171785763&partnerID=8YFLogxK
U2 - 10.1007/s00208-023-02718-3
DO - 10.1007/s00208-023-02718-3
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AN - SCOPUS:85171785763
SN - 0025-5831
VL - 389
SP - 3181
EP - 3229
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 3
ER -