KS-群胚与逆半群作用相关的KS-交叉积
KS-Groupoids and KS-Crossed Products associated with Inverse Semigroup Actions
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- Department of Mathematics, Faculty of Science and Technology, Keio University（庆应义塾大学理工学部数学系）
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中文总结 AI 辅助
本文针对逆半群在局部紧Hausdorff空间上的作用构造KS-群胚，给出Paterson定理的动力学版本，证明交叉积与群胚C*-代数典范同构，并研究其拓扑性质、函子性与泛性。
中文摘要 AI 辅助
对于逆半群$S$在局部紧Hausdorff空间$X$上的一个作用，我们构造了一个étale群胚$S\ltimes X^\mathrm{KS}$，称为与该作用相关的KS-群胚。此构造可视为逆半群泛群胚构造的动力学类比。我们提供了Paterson定理的动力学版本，该定理指出（在Khoshkam和Skandalis意义下的）$C_0(X)$的满交叉积和约化交叉积分别典范同构于$S\ltimes X^\mathrm{KS}$的满群胚C*-代数和约化群胚C*-代数。我们进一步研究了KS-群胚的一些拓扑性质、函子性和泛性。
英文摘要
For an action of an inverse semigroup $S$ on a locally compact Hausdorff space $X$, we construct an étale groupoid $S\ltimes X^\mathrm{KS}$, called the KS-groupoid associated with the action. This construction may be viewed as a dynamical analogue of the construction of universal groupoids for inverse semigroups. We provide a dynamical version of Paterson's theorem which states that the full and reduced crossed products (in the sense of Khoshkam and Skandalis) of $C_0(X)$ are canonically isomorphic to the full and reduced groupoid C*-algebras of $S\ltimes X^\mathrm{KS}$, respectively. We further investigate some topological properties, functoriality and universality of KS-groupoids.
