论文标题
在正式的Hilbert-Schmidt稳定组上
On amenable Hilbert-Schmidt stable groups
论文作者
论文摘要
我们从几个角度检查了离散符合组的Hilbert-Schmidt稳定性（HS稳定性）。我们提供了一个简短的基本证据，表明有限生成的nilpotent组是hs稳定的。我们通过显示HS稳定性在中心扩展下的HS稳定性的持久性由有限的中心商保留，但通常不保留。我们给出了半程产品的HS稳定性$ g \rtimes_γ\ Mathbb {z} $，并用$ g $ abelian。我们使用它来构建有限生成的正式HS稳定组的第一个示例，该组不是排列稳定的。最后，事实证明，对于符合性组而言，柔性HS稳定性等于HS稳定性，并且非常灵活的HS稳定性等于最大的几乎几乎是周期性。我们的工作与最近的左图和维格多维奇的预印本有些重叠。我们在引言中详细介绍了这种重叠。在我们的工作重叠的地方，似乎我们采取了不同的方法来证明证据，我们认为两部作品相互补充。
We examine Hilbert-Schmidt stability (HS-stability) of discrete amenable groups from several angles. We give a short, elementary proof that finitely generated nilpotent groups are HS-stable. We investigate the permanence of HS-stability under central extensions by showing HS-stability is preserved by finite central quotients, but is not preserved in general. We give a characterization of HS-stability for semidirect products $G\rtimes_γ\mathbb{Z}$ with $G$ abelian. We use it to construct the first example of a finitely generated amenable HS-stable group which is not permutation stable. Finally, it is proved that for amenable groups flexible HS-stability is equivalent to HS-stability, and very flexible HS stability is equivalent to maximal almost periodicity. There is some overlap of our work with the very recent and very nice preprint of Levit and Vigdorovich. We detail this overlap in the introduction. Where our work overlaps it appears that we take different approaches to the proofs and we feel the two works compliment each other.
