|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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