AI 中文总结
研究包含不可数阿贝尔子群的离散群\(G\)的\(C^*(G)\)，证明其不具有提升性质（LP），不可数离散阿贝尔群\(G\)的\(C^*(G)\)有局部提升性质（LLP）但无LP，揭示LP与LLP对全离散群\(C^*\) - 代数不一致。
AI 中文摘要
在本笔记中，我们证明对于每个包含不可数阿贝尔子群的离散群\(G\)，\(C^*(G)\)不具有提升性质（LP）。因此，对于每个不可数离散阿贝尔群\(G\)，核代数\(C^*(G)\)具有局部提升性质（LLP）但不具有LP。这表明对于全离散群\(C^*\) - 代数，LP和LLP不一致。
英文摘要
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.
Comments7 pages, comments welcome
