Document Type

Article

Publication Date

7-2014

DOI

http://dx.doi.org/10.1090/S0002-9947-2014-06146-1

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.

Copyright Statement

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: http://creativecommons.org/licenses/by-nc-nd/4.0/. doi: 10.1090/S0002-9947-2014-06146-1

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