傅里叶代数中的Leinert集和可补理想
Leinert sets and complemented ideals in Fourier algebras
摘要：
设$G$是一个局部紧群.我们将展示如何补充理想的傅立叶代数$A(G)$的$G$自然产生的一类薄集被称为Leinert集。此外，我们还提出了一个明确的例子，一个封闭的理想在$A(\mathbb{F}_{N})$，$N \ge 2$生成器上的自由群，这是补充在$A(\mathbb{F}_{N})$，但它不是完全补充。然后，通过对由Leinert集产生的限制代数建立一个适当的扩张结果，证明了几乎连通群$G$中的每一个可补理想都是完全可补的，并且几乎连通群$G$是可解的.
英文摘要：
Let $G$ be a locally compact group. We show how complemented ideals in the Fourier algebra $A(G)$ of $G$ arise naturally from a class of thin sets known as Leinert sets. Moreover, we also present an explicit example of a closed ideal in $A(\mathbb{F}_{N})$, the free group on $N \ge 2$ generators, that is complemented in $A(\mathbb{F}_{N})$ but it is not completely complemented. Then by establishing an appropriate extension result for restriction algebras arising from Leinert sets, we show that any almost connected group $G$ for which every complemented ideal in $A(G)$ is also completely complemented must be amenable.
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