Automorphisms of corona algebras, and group cohomology

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 in corpus (3)

• Countable saturation of corona algebras
• Reduced products of UHF algebras under forcing axioms
• Trivial automorphisms

Cited by in corpus (9)

• Countable saturation of corona algebras
• Saturation and elementary equivalence of C*-algebras
• Logic and operator algebras
• Rigidity of continuous quotients
• Forcing axioms and coronas of $C^{\ast }$-algebras
• Reduced products of UHF algebras under forcing axioms
• Logic and ${\mathrm{C}}^{\ast }$-algebras: set theoretical dichotomies in the theory of continuous quotients
• Corona Rigidity
• Isomorphisms of quotients of FDD-algebras