## Automorphisms of corona algebras, and group cohomology

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- by Samuel Coskey and Ilijas Farah PDF
- Trans. Amer. Math. Soc.
**366**(2014), 3611-3630 Request permission

## Abstract:

In 2007 Phillips and Weaver showed that, assuming the Continuum Hypothesis, there exists an outer automorphism of the Calkin algebra. (The Calkin algebra is the algebra of bounded operators on a separable complex Hilbert space, modulo the compact operators.) In this paper we establish that the analogous conclusion holds for a broad family of quotient algebras. Specifically, we will show that assuming the Continuum Hypothesis, if $A$ is a separable algebra which is either simple or stable, then the corona of $A$ has nontrivial automorphisms. We also discuss a connection with cohomology theory, namely, that our proof can be viewed as a computation of the cardinality of a particular derived inverse limit.## References

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## Additional Information

**Samuel Coskey**- Affiliation: The Fields Institute, 222 College Street, Toronto, Ontario, Canada M5T 3J1 — and — Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3
- Address at time of publication: Department of Mathematics, Boise State University, 1910 University Drive, Boise, Idaho 83725
- Email: scoskey@nylogic.org
**Ilijas Farah**- Affiliation: Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3 — and — Matematicki Institut, Kneza Mihaila 34, Belgrade, Serbia
- MR Author ID: 350129
- Email: ifarah@yorku.ca
- Received by editor(s): August 13, 2012
- Published electronically: March 19, 2014
- Additional Notes: The second author was partially supported by NSERC
- © Copyright 2014
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**366**(2014), 3611-3630 - MSC (2010): Primary 46L40; Secondary 46L05, 03E50
- DOI: https://doi.org/10.1090/S0002-9947-2014-06146-1
- MathSciNet review: 3192609