论文标题
某些特殊的核尺寸用于某些交叉产品$ {\ rm c^*} $ - 代数
Certain tracially nuclear dimensional for certain crossed product ${\rm C^*}$-algebras
论文作者
论文摘要
令$ω$为一类Unital $ {\ rm c^*} $ - 代数，该代数为Moat $ n $的第二种类型的Tracial核尺寸（或最多具有tracial核尺寸$ n $）。令$ a $为无限的尺寸简单$ {\ rm c^*} $ - 代数，使得$ a $在$ω$中是零散的。然后$ {\ rm t^2dim_ {nuc}}（a）\ leq n $（或$ {\ rm tdim_ {nuc}}}（a）\ leq n $）。作为一个应用程序，让$ a $为无限的简单简单可分离的unital $ {\ rm c^*} $ - 带有$ {\ rm t^2dim_ {nuc}}}（a）\ leq n $（或$ {\ rm tdim_ {nuc}}}（a nuc}}（a a a a））的代数。假设$α：g \ to {\ rm aut}（a）$是$ a $ a $ a $ a $ a $ g $的动作，该$ a $具有Tracial rokhlin属性。然后$ {\ rm t^2dim_ {nuc}}（{{{\ rm c^*}（g，a，a，α）}）\ leq n $（或$ {\ rm tdim_ {nuc {nuc}} $（{{{{\ rm c^*} $（{\ rm c^*}（g，g，a，a，a，α）}）。
Let $Ω$ be a class of unital ${\rm C^*}$-algebras which have the second type tracial nuclear dimensional at moat $n$ (or have tracial nuclear dimensional at most $n$). Let $A$ be an infinite dimensional unital simple ${\rm C^*}$-algebra such that $A$ is asymptotical tracially in $Ω$. Then ${\rm T^2dim_{nuc}}(A)\leq n$ (or ${\rm Tdim_{nuc}}(A)\leq n$). As an application, let $A$ be an infinite dimensional simple separable amenable unital ${\rm C^*}$-algebra with ${\rm T^2dim_{nuc}}(A)\leq n$ (or ${\rm Tdim_{nuc}}(A)\leq n$). Suppose that $α:G\to {\rm Aut}(A)$ is an action of a finite group $G$ on $A$ which has the tracial Rokhlin property. Then ${\rm T^2dim_{nuc}}({{\rm C^*}(G, A,α)})\leq n$ (or ${\rm Tdim_{nuc}}$ $({{\rm C^*}(G, A,α)})\leq n$).
