We show that all values in the interval $[0,{\pi }/{2}]$ can be attained as interior angles between intermediate subalgebras (as introduced by Bakshi and the first named author [‘Lattice of intermediate subalgebras’, J. Lond. Math. Soc. (2)104(2) (2021), 2082–2127]) of a certain inclusion of simple unital $C^*$ -algebras. We also calculate the interior angles between intermediate crossed product subalgebras of any inclusion of crossed product algebras corresponding to any action of a countable discrete group and its subgroups on a unital $C^*$ -algebra.

中文翻译：

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关于中间子代数之间的内角的可能值

我们证明区间内的所有值 $[0,{\pi }/{2}]$ 可以作为中间子代数之间的内角来获得（如 Bakshi 和第一作者 ['中间子代数的格',J·隆德. 数学。苏克。(2)104(2) (2021), 2082–2127]) 的一定包含简单单位 $C^*$ -代数。我们还计算与可数离散群及其子群在单位上的任何作用相对应的交叉积代数的任何包含的中间交叉积子代数之间的内角 $C^*$ -代数。