发表机构
University of Białystok; Georg-August-Universität Göttingen（比亚韦斯托克大学; 哥廷根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文刻画C*-不可约正则包含，建立中间C*-代数与子群的双射（推广伽罗瓦对应），并利用理想检测给出非周期性的等价条件，应用于Cuntz-Pimsner代数与图C*-代数。
AI 中文摘要
我们使用不同作者考虑的多组不同条件来刻画C*-不可约正则C*-包含。特别地，我们证明所有C*-不可约正则包含$A\subseteq B$均可由离散群上的外Fell丛$(B_{g})_{g\in G}$建模，其单位纤维$A=B_1$是简单的。在此情形下，我们证明了中间C*-代数$A\subseteq C \subseteq B$与$G$的子群$H$之间存在双射。这推广了Cameron-Smith建立的离散群作用约化交叉积的伽罗瓦对应。我们将其与Izumi和Mukohara关于紧交换群作用不动点代数的伽罗瓦对应，以及Echterhoff-Rørdam考虑的约化交叉积中不动点代数的混合包含联系起来。此外，利用Geffen-Ursu的一个近期结果，我们证明对于$\mathbb{T}$或$\mathbb{Z}/p$（$p>0$为无平方因子数）的作用，不动点子代数$A\subseteq B$的包含是非周期的当且仅当$A$检测$B$中的理想。我们应用此结果给出来自Cuntz-Pimsner代数的C*-不可约包含的例子，包括由自同态或转移算子给出的交叉积。特别地，我们刻画了图C*-代数的核子代数何时是C*-不可约的。最后，我们证明一般正则拓扑分次C*-包含$A\subseteq B$是非周期的，并且具有唯一的伪期望，前提是$A$检测$B$的所有中间C*-代数中的理想。这部分回答了Pitts-Zarikian的一个问题。
英文摘要
We characterise C*-irreducible regular C*-inclusions using a number of different conditions considered by different authors. In particular, we show that all C*-irreducible regular inclusions $A\subseteq B$ are modelled by outer Fell bundles $(B_{g})_{g\in G}$ over discrete groups with a simple unit fibre $A=B_1$. In this case, we prove a bijection between intermediate C*-algebras $A\subseteq C \subseteq B$ and subgroups $H$ of $G$. This extends the Galois correspondence for reduced crossed products by discrete group actions established by Cameron-Smith. We relate it to the Galois correspondences of Izumi and Mukohara for fixed-point algebras of actions of compact abelian groups, and the mixed inclusion of a fixed-point algebra in a reduced crossed product considered by Echterhoff-Rørdam. In addition, using a recent result of Geffen-Ursu, we show that the inclusion of a fixed-point subalgebra $A\subseteq B$ of an action of $\mathbb{T}$ or $\mathbb{Z}/p$ for a square-free number $p>0$ is aperiodic if and only if $A$ detects ideals in $B$. We apply this to give examples of C*-irreducible inclusions coming from Cuntz-Pimsner algebras, including crossed products by endomorphisms or transfer operators. In particular, we characterise when a core subalgebra of a graph C*-algebra is C*-irreducible. Lastly, we show that a general regular topologically graded C*-inclusion $A\subseteq B$ is aperiodic and has a unique pseudo-expectation provided $A$ detects ideals in all intermediate C*-algebras of $B$. This partially answers a question by Pitts-Zarikian.
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