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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On approximately inner automorphisms of certain crossed product $ C\sp *$-algebras


Authors: Marius Dădărlat and Cornel Pasnicu
Journal: Proc. Amer. Math. Soc. 110 (1990), 383-385
MSC: Primary 46L55; Secondary 18F25, 46L40
MathSciNet review: 1021897
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Abstract: Let $ G$ be a compact connected topological group having a dense subgroup isomorphic to $ {\mathbf{Z}}$. Let $ C(G)\mathop \rtimes \limits_ \propto {\mathbf{Z}}$ be the crossed product $ {C^ * }$-algebra of $ C(G)$ with $ {\mathbf{Z}}$, where $ {\mathbf{Z}}$ acts on $ G$ by rotations. Automorphisms of $ C(G)\mathop \rtimes \limits_ \propto {\mathbf{Z}}$ leaving invariant the canonical copy of $ C(G)$ are shown to be approximately inner iff they act trivially on $ {K_1}(C(G)\mathop \rtimes \limits_ \propto {\mathbf{Z}})$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1021897-4
PII: S 0002-9939(1990)1021897-4
Article copyright: © Copyright 1990 American Mathematical Society



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