We compute the nuclear dimension of separable, simple, unital, nuclear, \({\mathcal {Z}}\)-stable \(\mathrm {C}^*\)-algebras. This makes classification accessible from \({\mathcal {Z}}\)-stability and in particular brings large classes of \(\mathrm {C}^*\)-algebras associated to free and minimal actions of amenable groups on finite dimensional spaces within the scope of the Elliott classification programme.

中文翻译：

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简单$$ \ mathrm {C} ^ * $$ C ∗-代数的核维

我们计算可分离，简单，单位，核，\（{\ mathcal {Z}} \）- stable \（\ mathrm {C} ^ * \）-代数的核维数。这使得分类可以从\（{\ mathcal {Z}} \）-稳定性进行访问，特别是带来了大类的\（\ mathrm {C} ^ * \）-代数，这些代数与有限维上可适应组的自由和最小作用相关Elliott分类程序范围内的空格。