Computably strongly self-absorbing C*-algebras

TL;DR

This paper introduces the concept of computably strongly self-absorbing C*-algebras and demonstrates that several key examples, including the Jiang-Su algebra, possess this property, extending Elliott's approximate intertwining argument to a computable setting.

Contribution

It defines computably strongly self-absorbing C*-algebras and proves that important examples like , , and Z are computably strongly self-absorbing, with Z having a computable presentation.

Findings

 and  are computably strongly self-absorbing.

The Jiang-Su algebra Z has a computable presentation.

The results extend Elliott's approximate intertwining argument to a computable framework.

Abstract

We introduce the notion of a computably strongly self-absorbing C*-algebra and show that the following C*-algebras are computably strongly self-absorbing: the Cuntz algebras $\mathcal{O}_2$ and $\mathcal{O}_\infty$, the UHF algebra $M_{\mathfrak{n}}(\mathbb{C})$ and the tensor product $M_{\mathfrak{n}}(\mathbb{C})\otimes \mathcal{O}_\infty$, where $\mathfrak{n}$ is a supernatural number of infinite type with computably enumerable support, and the Jiang-Su algebra $\mathcal{Z}$. In connection with the last example, we show that $\mathcal{Z}$ has a computable presentation. The results above are a special instance of a computable version of the standard approximate intertwining argument due to Elliott.