Strongly self-absorbing $C^*$-algebras and Fraïssé limits

Abstract

We show that the Fraïssé limit of a category of unital separable C * -algebras which is sufficiently closed under tensor products of its objects and morphisms is strongly self-absorbing, given that it has approximate inner halfflip. We use this connection between Fraïssé limits and strongly self-absorbing C * -algebras to give a self-contained and rather elementary proof for the well known fact that the Jiang-Su algebra is strongly self-absorbing.

Nonseparable CCR algebras

“…Apparently the simplest instance of Question 5.1 not resolved by our Theorem 1 is the case of p prime M p (C). Probably the most interesting case is when A is the Jiang-Su algebra Z, whose Elliott invariant is equal to that of the complex numbers (see [15], also [12] and [17] for most recent treatments).…”