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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.

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First published in Transactions of the American Mathematical Society in volume 366, issue 7 in 2014. Published by the American Mathematical Society. This work is provided under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 license. Details regarding the use of this work can be found at: doi: 10.1090/S0002-9947-2014-06146-1

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