Calkin algebra, Kazhdan's property (T), strongly self-absorbing C*-algebras
Abstract
The Calkin algebra is not isomorphic to the corona of the stabilization of the Cuntz algebra~${\mathcal O}_\infty$, any other Kirchberg algebra, or even the corona of the stabilization of any unital, ${\mathcal Z}$-stable ${\mathrm C}^*$-algebra. The proof relies on properties of relative commutants of separable ${\mathrm C}^*$-subalgebras.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2022
- DOI:
- 10.48550/arXiv.2208.12301
- arXiv:
- arXiv:2208.12301
- Bibcode:
- 2022arXiv220812301F
- Keywords:
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- Mathematics - Operator Algebras
- E-Print:
- The proof of Proposition 2.1 (now Proposition 2.3) is now given in greater detail, and the entire section 2 has been revised. THe proof of Lemma 4.3 is now also given in more detail