发表机构
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 中文总结
本文构造了检测单位C*-代数上迹态可迹性的Hochschild上循环，并给出了嵌入超有限II1因子超幂的等价刻画，证明了可迹性使Christensen-Sinclair二上循环成为上边界。
AI 中文摘要
我们构造了一个有界的 Hochschild 一上循环，它检测单位 C*-代数上迹态的可迹性。对于任意迹，该构造使用一个包含 GNS 表示作为直和项的忠实表示。当 τ 是忠实的，Hτ=L2(A,τ)，且 J 是标准共轭时，该上循环具有特别简单的形式 δτ(a)(x)=Jπτ(a*)Jx-xJπτ(a*)J。它在自然 Banach A-双模中是内蕴的当且仅当 τ 是可迹的。我们还给出了嵌入超有限 II1 因子的超幂的相应重述。最后，对于忠实迹，我们研究了 Christensen-Sinclair 二上循环的 C*-代数变体，并证明了，连同所有可容许性细节，可迹性使得该上循环成为上边界。
英文摘要
We construct a bounded Hochschild one-cocycle which detects amenability of tracial states on unital C*-algebras. For an arbitrary trace the construction uses a faithful representation containing the GNS representation as a direct summand. When \(τ\) is faithful, \(H_τ=L^2(A,τ)\), and \(J\) is the canonical conjugation, the cocycle has the particularly simple form \[ δ_τ(a)(x) =Jπ_τ(a^*)Jx-xJπ_τ(a^*)J. \] It is inner in a natural Banach \(A\)-bimodule if and only if \(τ\) is amenable. We also give the corresponding reformulation of embeddability into an ultrapower of the hyperfinite \(\mathrm{II}_1\) factor. Finally, for faithful traces we study a C*-algebraic variant of the Christensen--Sinclair two-cocycle and prove, with all admissibility details, that amenability makes this cocycle a coboundary.
Comments11 pages, presubmission
