TY - JOUR

T1 - C*-stability of discrete groups

AU - Eilers, Soren

AU - Shulman, Tatiana

AU - Sorensen, Adam P. W.

PY - 2020

Y1 - 2020

N2 - A group may be considered C*-stable if almost representations of the group in a C*-algebra are always close to actual representations. We initiate a systematic study of which discrete groups are C*-stable or only stable with respect to some subclass of C*-algebras, e.g. finite dimensional C*-algebras. We provide criteria and invariants for stability of groups and this allows us to completely determine stability/non-stability of crystallographic groups, surface groups, virtually free groups, and certain Baumslag-Solitar groups. We also show that among the non-trivial finitely generated torsion-free 2-step nilpotent groups the only C*-stable group is Z. (C) 2020 Elsevier Inc. All rights reserved.

AB - A group may be considered C*-stable if almost representations of the group in a C*-algebra are always close to actual representations. We initiate a systematic study of which discrete groups are C*-stable or only stable with respect to some subclass of C*-algebras, e.g. finite dimensional C*-algebras. We provide criteria and invariants for stability of groups and this allows us to completely determine stability/non-stability of crystallographic groups, surface groups, virtually free groups, and certain Baumslag-Solitar groups. We also show that among the non-trivial finitely generated torsion-free 2-step nilpotent groups the only C*-stable group is Z. (C) 2020 Elsevier Inc. All rights reserved.

KW - C-algebra of a discrete group

KW - Almost commuting matrices

KW - Noncommutative CW-complexes

KW - Crystallographic groups

KW - Virtually free groups

KW - REPRESENTATIONS

KW - SEMIPROJECTIVITY

KW - OPERATORS

KW - MATRICES

KW - ALGEBRA

U2 - 10.1016/j.aim.2020.107324

DO - 10.1016/j.aim.2020.107324

M3 - Journal article

VL - 373

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

M1 - 107324

ER -