一致有界表示的相对性质(T)
Relative property (T) for uniformly bounded representations
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中文总结 AI 辅助
该研究将全群C*-代数、傅里叶-斯蒂尔杰斯代数推广到一致有界表示语境，刻画相对性质(T)，并将Serre定理推广到一致有界语境，证明半直积的相对性质(T)等价于其一致有界版本。
中文摘要 AI 辅助
对于局部紧群G及其闭子群H构成的对(G,H)，我们为一致有界表示引入了全群C*-代数和傅里叶-斯蒂尔杰斯代数的类似版本。我们利用这些对象，在更一般的语境下通过Kazhdan投影和不变均值来刻画相对性质(T)。我们还证明，对于形如G=H⋉N的半直积（其中N为幂零群），对(G,N)的相对性质(T)等价于其一致有界版本。我们首先在N为阿贝尔群时证明该结果，随后研究相对性质(T)在模中心子群的商群下的行为，从而将Serre定理推广到一致有界语境。
英文摘要
For pairs $(G,H)$, where $G$ is a locally compact group and $H$ is a closed subgroup of $G$, we introduce analogous versions of the full group $\mathrm{C}^*$-algebra and the Fourier--Stieltjes algebra for uniformly bounded representations. We use these objects to characterise relative property (T) in this more general setting in terms of Kazhdan projections and invariant means. We also show that, for semidirect products of the form $G=H\ltimes N$, where $N$ is a nilpotent group, relative property (T) for the pair $(G,N)$ is equivalent to its uniformly bounded version. We first prove this result when $N$ is abelian, and then proceed by studying the behaviour of relative property (T) under quotients by central subgroups, thereby extending a theorem of Serre to the uniformly bounded setting.
发表机构
- University of Maryland（马里兰大学）
- Universidad de La Frontera（拉弗龙特拉大学）
机构由 AI 辅助整理，请以论文原文为准。
