可数离散 amenable 群的全群 $C^*$-代数为 strong NF 的归纳证明
An induction proof of strong NF\ for amenable group $C^*$-algebras
- University of Toronto（多伦多大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过表示论与迹分解方法，归纳证明了可数离散 amenable 群的全群 $C^*$-代数为 strong NF，并提供了直接变体及两证明的共有步骤。
AI中文摘要：
我们给出了一个证明：可数离散 amenable 群的全群 $C^*$-代数是 strong NF。该表示论构造使用了精确序列，其核为 hyper-FC 根，商为极大 ICC 商。根上的极端不变迹诱导群的因子表示。正则根迹的 Choquet 分解选取一个分离族，其诱导迹支撑在通常的 FC-中心上。精确的扭曲交叉积商和序列 UCT 论证使其像拟对角化。忠实不可约替换随后提供内拟对角化所需的投影。我们还给出了一个直接的迹分解变体，并指出了两个证明共有的步骤。
英文摘要：
We give a proof that the full group $C^*$-algebra of a countable discrete amenable group is strong NF. The representation-theoretic construction uses the exact sequence whose kernel is the hyper-FC radical and whose quotient is the maximal ICC quotient. Extreme invariant traces on the radical induce factorial representations of the group. A Choquet decomposition of the regular radical trace selects a separating family whose induced traces are supported on the ordinary FC-centre. Exact twisted crossed-product quotients and a sequential UCT argument make their images quasidiagonal. Faithful irreducible replacements then supply the projections required for inner quasidiagonality. We also give a direct trace-decomposition variant and identify the steps shared by the two proofs.
