Strongly self-absorbing C*-algebras

Andrew S. Toms; Wilhelm Winter

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arXiv · math/0502211

Strongly self-absorbing C*-algebras

Andrew S. Toms·Wilhelm Winter

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Abstract

Say that a separable, unital C*-algebra D is strongly self-absorbing if there exists an isomorphism $ϕ: D \to D \otimes D$ such that $ϕ$ and $id_D \otimes 1_D$ are approximately unitarily equivalent $*$-homomorphisms. We study this class of algebras, which includes the Cuntz algebras $\mathcal{O}_2$, $\mathcal{O}_{\infty}$, the UHF algebras of infinite type, the Jiang--Su algebra Z and tensor products of $\Oh_{\infty}$ with UHF algebras of infinite type. Given a strongly self-absorbing C*-algebra D we characterise when a separable C*-algebra absorbs D tensorially (i.e., is D-stable), and prove closure properties for the class of separable D-stable C*-algebras. Finally, we compute the possible K-groups and prove a number of classification results which suggest that the examples listed above are the only strongly self-absorbing C*-algebras.

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BibTeX RIS

Andrew S. Toms, Wilhelm Winter. 2005-08-31. Strongly self-absorbing C*-algebras. https://arxiv.org/abs/math/0502211

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