发表机构
Purdue University; University of Oregon（普渡大学; 俄勒冈大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入C*-动力系统的动力比较半径，给出其有序半群定义，并证明其与Kerr动力比较的关系，以及有限群作用下的不等式与等式结果。
AI 中文摘要
我们基于动力Cuntz半群，引入了单位C*-代数的比较半径 $\operatorname{rc} (A)$ 的动力版本 $\operatorname{rc} (A, \alpha)$。我们还给出了一个内在的有序半群定义，当 $A$ 是剩余稳定有限的时，该定义与 $\operatorname{rc} (A, \alpha)$ 一致，并且对于具有单射单位映射的等变直接极限是下半连续的。我们构造了 $G = \mathbb{Z} / 2 \mathbb{Z}$ 在简单单位AH代数上的作用 $\alpha$，使得 $\operatorname{rc} (A, \alpha)$ 严格介于 $\operatorname{rc} (A)$ 和 $\operatorname{rc} (A) / \operatorname{card} (G)$ 之间，以及有限群 $G$ 在单位C*-代数上的作用 $\alpha$，使得 $\operatorname{rc} (A, \alpha)$ 严格介于 $\operatorname{rc} (A)$ 和 $\operatorname{rc} (C^* (G, A, \alpha))$ 之间。对于可数离散群 $G$ 在零维紧致可度量空间 $X$ 上的极小作用，我们证明了 $\operatorname{rc} (C (X), \alpha) = 0$ 当且仅当该作用具有Kerr所定义的动力比较。对于简单单位稳定有限C*-代数上的有限群作用，假设弱迹Rokhlin性质，我们得到 $\operatorname{rc} (A, \alpha) \leq \operatorname{rc} (A) / \operatorname{card} (G)$，并且假设弱迹严格近似内性，我们得到 $\operatorname{rc} (A, \alpha) = \operatorname{rc} (A)$。
英文摘要
We introduce a dynamical version $\operatorname{rc} (A, α)$ of the radius of comparison $\operatorname{rc} (A)$ of a unital C*-algebra, based on the dynamical Cuntz semigroup. We also give an intrinsic ordered semigroup definition, which agrees with $\operatorname{rc} (A, α)$ when $A$ is residually stably finite, and is lower semicontinuous for equivariant direct limits with injective unital maps. We construct actions $α$ of $G = \mathbb{Z} / 2 \mathbb{Z}$ on simple unital AH~algebras for which $\operatorname{rc} (A, α)$ lies strictly between $\operatorname{rc} (A)$ and $\operatorname{rc} (A) / \operatorname{card} (G)$, and actions $α$ of a finite group $G$ on unital C*-algebras for which $\operatorname{rc} (A, α)$ lies strictly between $\operatorname{rc} (A)$ and $\operatorname{rc} (C^* (G, A, α))$. For a minimal action of a countable discrete group $G$ on a zero dimensional compact metrizable space $X$, we prove that $\operatorname{rc} (C (X), α) = 0$ if and only if the action has dynamical comparison as defined by Kerr. For finite group actions on simple unital stably finite C*-algebras, assuming the weak tracial Rokhlin property, we get $\operatorname{rc} (A, α) \leq \operatorname{rc} (A) / \operatorname{card} (G)$, and assuming weak tracial strict approximate innerness, we get $\operatorname{rc} (A, α) = \operatorname{rc} (A)$.
Comments68 pages; comments welcome
