Calkin algebra, Kazhdan's property (T), strongly selfabsorbing 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:

arXiv eprints
 Pub Date:
 August 2022
 DOI:
 10.48550/arXiv.2208.12301
 arXiv:
 arXiv:2208.12301
 Bibcode:
 2022arXiv220812301F
 Keywords:

 Mathematics  Operator Algebras
 EPrint:
 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