Local Hilbert--Schmidt stability
We introduce a notion of local Hilbert--Schmidt stability, motivated by the recent definition by Bradford of local permutation stability, and give examples of (non-residually finite) groups that are locally Hilbert--Schmidt stable but not Hilbert--Schmidt stable. For amenable groups, we provide a cr...
Saved in:
Main Authors | , , |
---|---|
Format | Journal Article |
Language | English |
Published |
24.07.2023
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | We introduce a notion of local Hilbert--Schmidt stability, motivated by the
recent definition by Bradford of local permutation stability, and give examples
of (non-residually finite) groups that are locally Hilbert--Schmidt stable but
not Hilbert--Schmidt stable. For amenable groups, we provide a criterion for
local Hilbert--Schmidt stability in terms of group characters, by analogy with
the character criterion of Hadwin and Shulman for Hilbert--Schmidt stable
amenable groups. Furthermore, we study the (very) flexible analogues of local
Hilbert--Schmidt stability, and we prove several results analogous to the
classical setting. Finally, we prove that infinite sofic, respectively
hyperlinear, property (T) groups are never locally permutation stable,
respectively locally Hilbert--Schmidt stable. This strengthens the result of
Becker and Lubotzky for classical stability, and answers a question of
Lubotzky. |
---|---|
DOI: | 10.48550/arxiv.2307.13155 |