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.
Categories: math.LO math.OA