群的均匀希尔伯特施密特稳定性

D. Akhtiamov, Alon Dogon
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引用次数: 6

摘要

如果任何映射$\varphi : \Gamma \to U(n)$几乎是酉表示(w.r.t.希尔伯特施密特范数)接近于相同维度的真正酉表示,则群$\Gamma$被称为一致HS稳定。给出了在有限生成的剩余有限群中一致HS稳定群的完全分类。讨论了剩余有限假设的必要性。一个类似的结果显示,只假设顺从。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On uniform Hilbert Schmidt stability of groups
A group $\Gamma$ is said to be uniformly HS stable if any map $\varphi : \Gamma \to U(n)$ that is almost a unitary representation (w.r.t. the Hilbert Schmidt norm) is close to a genuine unitary representation of the same dimension. We present a complete classification of uniformly HS stable groups among finitely generated residually finite ones. Necessity of the residual finiteness assumption is discussed. A similar result is shown to hold assuming only amenability.
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