Strongly self-absorbing $C^{\ast }$-algebras and Fraïssé limits

Abstract

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

This is the journal accepted version