Stability of group relations under small Hilbert–Schmidt perturbations

Entanglement in Non-local Games and the Hyperlinear Profile of Groups

“…In this section, we state our first definition of hyperlinear profile, along with some basic properties. The starting point is the following definition from, e.g., [Slo17] or [HS17].…”

II1 FACTORS WITH EXOTIC CENTRAL SEQUENCE ALGEBRAS

“…The class of W * -tracially stable groups contains all abelian and free groups as well as other classes of both amenable and non-amenable groups; see [17]. As an immediate consequence of Proposition C, we deduce that the class of W * -tracially stable groups is closed under taking the direct product with a W * -tracially stable amenable group.…”

“…In recent years, there has been growing interest in the study of the notion of stability for groups (see the survey [44]). As a byproduct of the methods developed in this article, we obtain two applications to the notion of tracial stability for countable groups, formalized recently in [17] (see also [16]). Definition 1.7 [17,Definition 3].…”

“…As a byproduct of the methods developed in this article, we obtain two applications to the notion of tracial stability for countable groups, formalized recently in [17] (see also [16]). Definition 1.7 [17,Definition 3]. A countable group is W * -tracially stable if for any sequence (M n , τ n ), n ∈ N, of tracial von Neumann algebras and any homomorphism ϕ :…”

Free products with amalgamation over central 𝐶*-subalgebras

“…This gives us a wealth of examples of RFD C * -algebras coming from discrete groups. Beyond these, examples of groups with RFD C * -algebras include full group C * -algebras of nonabelian free groups [8], virtually abelian groups [31], surface groups and fundamental groups of closed hyperbolic 3-manifolds that fiber over the circle [25], and many 1-relator groups with non-trivial center [19].…”