Fourier代数的算子双平坦性与子群的逼近指标
Operator biflatness of the Fourier algebra and approximate indicators for subgroups
摘要：
研究了局部紧群$G$的Fourier代数$A(G)$在量子化Banach同调意义下是否是双平坦的.在我们的调查中的一个核心作用是发挥了一个闭子群的子群$G$的近似指标的概念：傅立叶代数是运营商biflat每当对角线在$G \times G$有一个近似指标。虽然我们一直无法解决的问题，是否$A(G)$总是运营商双平坦的，我们表明，$G = SL(3,C)$，对角线在$G \times G$未能有一个近似的指标。
英文摘要：
We investigate if, for a locally compact group $G$, the Fourier algebra $A(G)$ is biflat in the sense of quantized Banach homology. A central role in our investigation is played by the notion of an approximate indicator of a closed subgroup of $G$: The Fourier algebra is operator biflat whenever the diagonal in $G \times G$ has an approximate indicator. Although we have been unable to settle the question of whether $A(G)$ is always operator biflat, we show that, for $G = SL(3,C)$, the diagonal in $G \times G$ fails to have an approximate indicator.
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