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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On automorphisms of L.C. groups


Author: Justin Peters
Journal: Proc. Amer. Math. Soc. 65 (1977), 347-350
MSC: Primary 22D45
DOI: https://doi.org/10.1090/S0002-9939-1977-0450457-2
MathSciNet review: 0450457
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Abstract: The left regular representation $ \lambda $ of a locally compact group G generates a $ {W^\ast}$-algebra $ \mathcal{R}(\lambda )$, and each topological automorphism $ \tilde \alpha $ of G has a natural extension to an automorphism $ \tilde \alpha $ of $ \mathcal{R}(\lambda )$. It is proved that an automorphism $ \beta $ of $ \mathcal{R}(\lambda )$ is of the form $ \beta = \tilde \alpha $ for $ \alpha \in {\operatorname{Aut}}(G)$ iff $ \beta $ leaves a certain cone in $ \mathcal{R}(\lambda )$ invariant.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0450457-2
Keywords: Automorphism, $ {W^\ast}$-algebra, Fourier algebra, measure algebra, group character
Article copyright: © Copyright 1977 American Mathematical Society