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Uncountable Abelian Group C*-algebras Fail the Lifting Property
arXiv Math
CC BY
이 매체는 공공·자유 라이선스로 본문을 직접 표시합니다.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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