AI 中文总结
研究对角维数的有限性与中间子\(C^*\)-代数的关系，通过获取中间子\(C^*\)-代数与对角组成的对的对角维数上界，推广了阿奇博尔德和库姆简关于\(AF\)-对角中间子代数的定理。
AI 中文摘要
我们证明，在李 - 廖 - 温特意义下的对角维数的有限性传递到中间子\(C^*\)-代数。具体而言，我们得到了\(C^*\)-对角中的中间子\(C^*\)-代数与对角组成的对的对角维数的一个上界，该上界根据环境对的对角维数和对角谱的覆盖维数来估计。这推广了阿奇博尔德和库姆简的一个定理，即\(AF\)-对角的中间子\(C^*\)-代数是\(AF C^*\)-代数。
英文摘要
We show that finiteness of diagonal dimension, in the sense of Li--Liao--Winter, passes to intermediate sub-C*-algebras. More specifically, we obtain an upper bound for the diagonal dimension of the pair of an intermediate sub-C*-algebra in a C*-diagonal together with the diagonal, which we estimate in terms of the diagonal dimension of the ambient pair and the covering dimension of the diagonal's spectrum. This generalizes a theorem of Archbold and Kumjian stating that intermediate sub-C*-algebras of AF-diagonals are AF C*-algebras.
Comments26 pages, comments welcome
