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Transactions of the American Mathematical Society

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A separable postliminal $ C\sp{\ast} $-algebra without maximal closed ideals


Author: H. Leptin
Journal: Trans. Amer. Math. Soc. 159 (1971), 489-496
MSC: Primary 46.65
DOI: https://doi.org/10.1090/S0002-9947-1971-0281016-1
MathSciNet review: 0281016
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Abstract: Let $ G$ be the free abelian group with a countable number of generators. We construct a separable locally compact $ G$-transformation space $ X$ without closed minimal invariant subsets, such that the corresponding $ {C^ \ast }$-algebra $ {C^ \ast }(G,X)$ has the properties mentioned in the title. Using $ X$ we also give an example of a transformation space $ (G,Z)$ without closed minimal invariant subset, on which $ G$ acts freely.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1971-0281016-1
Keywords: Locally compact transformation spaces, crossed products, transformation group $ {C^ \ast }$-algebras, generalized $ {L^1}$-algebras, structure spaces of groups and algebras
Article copyright: © Copyright 1971 American Mathematical Society

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