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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 algebrais the algebra of bounded operators on a separable complex Hilbert space,modulo the compact operators.) In this paper we establish that the analogousconclusion holds for a broad family of quotient algebras. Specifically, we willshow that assuming the Continuum Hypothesis, if $A$ is a separable algebrawhich is either simple or stable, then the corona of $A$ has nontrivialautomorphisms. We also discuss a connection with cohomology theory, namely,that our proof can be viewed as a computation of the cardinality of aparticular derived inverse limit.

Automorphisms of corona algebras, and group cohomology