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arXiv · 1808.06793

C*-stability of discrete groups

Søren Eilers·Tatiana Shulman·Adam P. W. Sørensen
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Abstract

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, finitely generated torsion-free step-2 nilpotent groups, surface groups, virtually free groups and certain Baumslag-Solitar groups.

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Søren Eilers, Tatiana Shulman, Adam P. W. Sørensen. 2018-08-21. C*-stability of discrete groups. https://arxiv.org/abs/1808.06793

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