发表机构
University of Haifa; University of Copenhagen（海法大学; 哥本哈根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对C*-代数领域，证明全交叉积的Hao-Ng同构不成立，分离出三类具体结构阻碍，为相关同构问题的进一步研究提供了关键依据。
AI 中文摘要
我们证明了全交叉积的Hao-Ng同构不成立。更确切地说，对于C*-代数$\boldsymbol{\textit{A}}$上的非退化C*-对应$X$，以及局部紧群$G$对$X$的广义规范作用$G \ni x$，我们分离出全交叉积与Cuntz-Pimsner C*-代数之间的典范交换$\boldsymbol{\textit{O}}_X \rtimes G \ncong \boldsymbol{\textit{O}}_{X \rtimes G}$的三个结构阻碍：第一个是缺乏超刚性，第二个是系数C*-代数$\boldsymbol{\textit{A}}$缺乏WEP，第三个是$G$对$\boldsymbol{\textit{A}}$的作用下全交叉积与约化交叉积不重合。
英文摘要
We show that the Hao-Ng isomorphism for full crossed products fails to hold. More precisely, for a non-degenerate $C^*$-correspondence $X$ over a $C^*$-algebra $\mathcal{A}$ and a generalized gauge action $G \curvearrowright X$ by a locally compact group $G$, we isolate three structural obstructions for the canonical commutation $\mathcal{O}_X\rtimes G \cong \mathcal{O}_{X\rtimes G}$ between full crossed product and Cuntz-Pimsner $C^*$-algebra. The first concerns hyperrigidity, the second concerns WEP of the coefficient $C^*$-algebra $\mathcal{A}$ for trivial actions, and the third concerns the coincidence of full and reduced crossed products by the action of $G$ on $\mathcal{A}$.
CommentsMinor revision. Reordered material on tensor algebras. Added acknowledgements. 18 pages including references
