A note on the orbit equivalence of injective actions

Xiangqi Qiang; Chengjun Hou

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arXiv · 2404.14002

A note on the orbit equivalence of injective actions

Xiangqi Qiang·Chengjun Hou

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Abstract

We characterise the groupoid $C^*$-algebras associated to the transformation groupoids of injective actions of discrete countable Ore semi-groups on compact topological spaces in terms of the reduced crossed product from the dual actions, and characterise the continuous orbit equivalence for injective actions by means of the transformation groupoids, as well as their reduced groupoid $C^*$-algebras. Finally, we characterize the injective action of semi-group on its compactifications.

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Xiangqi Qiang, Chengjun Hou. 2024-04-22. A note on the orbit equivalence of injective actions. https://arxiv.org/abs/2404.14002

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