Strongly self-absorbing $C^*$-algebras and Fra\"iss\'e limits

TL;DR

This paper establishes a link between Fra"issé limits of certain categories of unital separable $C^*$-algebras and strongly self-absorbing $C^*$-algebras, providing a new elementary proof that the Jiang-Su algebra is strongly self-absorbing.

Contribution

It demonstrates that Fra"issé limits with specific properties are strongly self-absorbing, offering a new proof for the Jiang-Su algebra's self-absorption.

Findings

Fra"issé limits of certain $C^*$-categories are strongly self-absorbing

The Jiang-Su algebra is shown to be strongly self-absorbing via this method

Provides an elementary proof for a well-known fact

Abstract

We show that the Fra\"iss\'e 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 half-flip. We use this connection between Fra\"iss\'e 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.