论文标题
广义的特特拉克近似C* - 代数
Generalized Tracially Approximated C*-algebras
论文作者
论文摘要
在本文中，我们介绍了一些广义曲折近似类别$ {\ rm c^*} $ - 代数。考虑一个$ \ Mathcal {z} $的unital $ {\ rm c^*} $ - 代数 - 吸收（或最多具有tracial核尺寸，或最多具有tracial核尺寸，或者拥有属性$ \ rm sp $，或者是$ m $ m $ - 最大的分区）。然后，$ a $是trac上是$ \ mathcal {z} $ - 吸收（分别吸收（分别具有曲折的核维度），对于任何简单的unital $ {\ rm c^*} $ - algebra $ a $ in comperiatiand of the property（$ n，m $）的属性是薄弱的（$ n，m $） - 几乎是分解的） C^*} $ - 代数。作为一个应用程序，让$ a $为无限尺寸的Unital简单$ {\ rm c^*} $ - 代数，让$ b $是$ a $的集中大型sibalgebra。如果$ b $是特殊的$ \ mathcal {z} $ - 吸收，则$ a $是特克萨利亚$ \ mathcal {z} $ - 吸收。该结果由Archey，Buck和Phillips在\ cite {ajn}中获得。
In this paper, we introduce some classes of generalized tracial approximation ${\rm C^*}$-algebras. Consider the class of unital ${\rm C^*}$-algebras which are tracially $\mathcal{Z}$-absorbing (or have tracial nuclear dimension at most $n$, or have the property $\rm SP$, or are $m$-almost divisible). Then $A$ is tracially $\mathcal{Z}$-absorbing (respectively, has tracial nuclear dimension at most $n$, has the property $\rm SP$, is weakly ($n, m$)-almost divisible) for any simple unital ${\rm C^*}$-algebra $A$ in the corresponding class of generalized tracial approximation ${\rm C^*}$-algebras. As an application, let $A$ be an infinite-dimensional unital simple ${\rm C^*}$-algebra, and let $B$ be a centrally large subalgebra of $A$. If $B$ is tracially $\mathcal{Z}$-absorbing, then $A$ is tracially $\mathcal{Z}$-absorbing. This result was obtained by Archey, Buck, and Phillips in \cite{AJN}.
