The ideal separation property for reduced group $C^*$-algebras

Are Austad; Hannes Thiel

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arXiv · 2408.14880

The ideal separation property for reduced group $C^*$-algebras

Are Austad·Hannes Thiel

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Abstract

We say that an inclusion of an algebra $A$ into a $C^*$-algebra $B$ has the ideal separation property if closed ideals in $B$ can be recovered by their intersection with $A$. Such inclusions have attractive properties from the point of view of harmonic analysis and noncommutative geometry. We establish several permanence properties of locally compact groups for which $L^1(G) \subseteq C^*_{\mathrm{red}}(G)$ has the ideal separation property.

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Are Austad, Hannes Thiel. 2024-08-27. The ideal separation property for reduced group $C^*$-algebras. https://arxiv.org/abs/2408.14880

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