论文标题
通过特殊性严格近似内部作用的交叉产物比较半径
The radius of comparison of the crossed product by a tracially strictly approximately inner action
论文作者
论文摘要
令$ g $为有限的组，让$ a $为无限的稳定稳定的简单的unital c*-algebra，让$α\ colon g \ to \ operatoratorname {aut}（a aut}（a）$是$ a $ a $ a $ a $ a $ a $ g $的traCallical ofical operatial operatornage {aut}（a）。然后，比较半径满足$ \ peratatorName {rc}（a）\ leq \ leq \ propatorName {rc} \ big（c^*（g，a，a，a，a，α）\ big）$，如果$ c^*（g，a，a，α）$很简单，然后简单，然后$ \ \ caperAtOrnAme {rc}（rc}（rc} a） c^*（g，a，α）\ big）\ leq \ operatotorname {rc}（a^α）$。此外，将$ a $ in $ c^*（g，a，α）$纳入了cuntz semigroup $ \ permatatorName {cu}（a）$的纯粹积极部分到其在$ \ operatoTornAme {cu} \ weft（c^*（c^*（c^*，a，a，α）$）中。如果$α$严格近似内部，则实际上$ \ operatorName {cu}（a）\ to \ operatotorName {cu} \ left（c^*（g，a，a，α）\ right）$是订购的semogroup同态范围。另外，对于每一个有限的$ g $，对于\ weft（0，\ frac {1} {\ propatotorname {card}（g）（g）} \ right）$，我们构造一个简单的可分开的Unital ah代数$ A $，具有稳定的稳定级别，并严格近似colon $ colon g colon g colon \ colon \ colon \ colon \ colon \ the \ the \ the \ the \ the \ the \ the \ the \ feration \ to \ feration \ tho \ fealorne \ tho \ ferator ^ （1）$α$是外部的，并且没有弱的曲折rokhlin属性。 （2）$ \ operatorname {rc}（a）= \ operatorname {rc} \ left（c^*（g，a，a，α）\ right）=η$。
Let $G$ be a finite group, let $A$ be an infinite-dimensional stably finite simple unital C*-algebra, and let $α\colon G \to \operatorname{Aut} (A)$ be a tracially strictly approximately inner action of $G$ on $A$. Then the radius of comparison satisfies $\operatorname{rc} (A) \leq \operatorname{rc} \big( C^*(G, A, α) \big)$ and if $C^*(G, A, α)$ is simple, then $\operatorname{rc} (A) \leq \operatorname{rc} \big( C^*(G, A, α) \big) \leq \operatorname{rc} (A^α)$. Further, the inclusion of $A$ in $C^*(G, A, α)$ induces an isomorphism from the purely positive part of the Cuntz semigroup $\operatorname{Cu} (A)$ to its image in $\operatorname{Cu} \left(C^*(G, A, α)\right)$. If $α$ is strictly approximately inner, then in fact $\operatorname{Cu} (A) \to \operatorname{Cu} \left(C^*(G, A, α) \right)$ is an ordered semigroup isomorphism onto its range. Also, for every finite group $G$ and for every $η\in \left(0, \frac{1}{\operatorname{card} (G)}\right)$, we construct a simple separable unital AH algebra $A$ with stable rank one and a strictly approximately inner action $α\colon G \to \operatorname{Aut} (A)$ such that: (1) $α$ is pointwise outer and doesn't have the weak tracial Rokhlin property. (2) $\operatorname{rc} (A) =\operatorname{rc} \left(C^*(G, A, α)\right)= η$.
