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 | 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. |
Publisher: | American Mathematical Society |
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