Uncountable Abelian Group C*-algebras Fail the Lifting Property

Miles Gould

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arXiv · 2607.20407

Uncountable Abelian Group C*-algebras Fail the Lifting Property

Miles Gould

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Abstract

In this note, we show that $C^*(G)$ fails the lifting property (LP) for every discrete group $G$ containing an uncountable abelian subgroup. Consequently, for every uncountable discrete abelian group $G$, the nuclear algebra $C^*(G)$ has the local lifting property (LLP) but fails the LP. This shows that the LP and the LLP do not coincide for full discrete group $C^*$-algebras.

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Miles Gould. 2026-07-22. Uncountable Abelian Group C*-algebras Fail the Lifting Property. https://arxiv.org/abs/2607.20407

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