关于中间子代数间内角的可能值

Pub Date : 2022-11-14 DOI:10.1017/s1446788723000058

V. Gupta, Deepika Sharma

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引用次数: 0

摘要

我们证明了区间$[0，{\pi}/{2}]$中的所有值都可以作为中间子代数(由Bakshi和第一作者[' Lattice of intermediate subalgebras '， J. Lond引入)之间的内角来获得。数学。Soc。(2)104(2)(2021)， 2082-2127])的简单一元$C^*$ -代数的一定包含。我们还计算了可数离散群及其子群在一元C^*$ -代数上的任意作用所对应的任意交叉积代数包含的中间交叉积子代数之间的内角。

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ON POSSIBLE VALUES OF THE INTERIOR ANGLE BETWEEN INTERMEDIATE SUBALGEBRAS

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.

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