Authors: Coskey, Samuel
Farah, Ilijas 
Title: Automorphisms of corona algebras, and group cohomology
Journal: Transactions of the American Mathematical Society
Volume: 366
Issue: 7
First page: 3611
Last page: 3630
Issue Date: 1-Jan-2014
Rank: M21
ISSN: 0002-9947
DOI: 10.1090/S0002-9947-2014-06146-1
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.
Publisher: American Mathematical Society

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