论文标题
对简单的tracyaly $ \ mathcal {z} $ - 吸收C*-Algebras的小组操作
Group actions on simple tracially $\mathcal{Z}$-absorbing C*-algebras
论文作者
论文摘要
我们表明，如果$ a $是一个简单的（不一定是单一的）$ \ mathcal {z} $ - 吸收c*-algebra和$α\ colon g \ to \ mathrm {aut}（a aut}（a）$是$ a $ a $ a $ a $ a $ a $ g $ a $ cross $ and poppers $ and poppers a的$ g $ a的动作代数$ a^α$是简单的，trac上$ \ nathcal {z} $ - 吸收，它们是$ \ Mathcal {z} $ - 如果此外，$ a $是可分离且核的，则稳定。对于包含物的所有中间c* - 代数，$ a^α\ subseteq a $和$ a \ subseteq c^*（g，a，a，α）$也相同。我们证明，如果$ a $是一种简单的trac上$ \ mathcal {z} $ - 吸收c*-algebra，那么，在有限的条件下，对称组$ s_m $ $ s_m $的置换作用是$ $ m $ m $ fold tensor $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a。我们为简单的C* - 代数的自动形态定义了弱的Tracial Rokhlin特性，我们表明 - 在轻度假设下 - （Tracial）$ \ Mathcal {Z} $ - 通过此类自动形态保留在交叉产品下的吸收。
We show that if $A$ is a simple (not necessarily unital) tracially $\mathcal{Z}$-absorbing C*-algebra and $α\colon G \to \mathrm{Aut} (A)$ is an action of a finite group $G$ on $A$ with the weak tracial Rokhlin property, then the crossed product $C^*(G, A,α)$ and the fixed point algebra $A^α$ are simple and tracially $\mathcal{Z}$-absorbing, and they are $\mathcal{Z}$-stable if, in addition, $A$ is separable and nuclear. The same conclusion holds for all intermediate C*-algebras of the inclusions $A^α\subseteq A$ and $A \subseteq C^*(G, A,α)$. We prove that if $A$ is a simple tracially $\mathcal{Z}$-absorbing C*-algebra, then, under a finiteness condition, the permutation action of the symmetric group $S_m$ on the minimal $m$-fold tensor product of $A$ has the weak tracial Rokhlin property. We define the weak tracial Rokhlin property for automorphisms of simple C*-algebras and we show that -- under a mild assumption -- (tracial) $\mathcal{Z}$-absorption is preserved under crossed products by such automorphisms.
