{"title":"Continuous Orbit Equivalence of Semigroup Actions","authors":"Xiang Qi Qiang, Cheng Jun Hou","doi":"10.1007/s10114-023-2608-6","DOIUrl":null,"url":null,"abstract":"<p>We introduce notions of continuous orbit equivalence and its one-sided version for countable left Ore semigroup actions on compact spaces by surjective local homeomorphisms, and characterize them in terms of the corresponding transformation groupoids and their operator algebras. In particular, we show that two essentially free semigroup actions on totally disconnected compact spaces are continuously orbit equivalent if and only if there is a canonical abelian subalgebra preserving <i>C</i>*-isomorphism between the associated transformation groupoid <i>C</i>*-algebras. We also give some examples of orbit equivalence, consider the special case of semigroup actions by homeomorphisms and relate continuous orbit equivalence of semigroup actions to that of the associated group actions.</p>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10114-023-2608-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We introduce notions of continuous orbit equivalence and its one-sided version for countable left Ore semigroup actions on compact spaces by surjective local homeomorphisms, and characterize them in terms of the corresponding transformation groupoids and their operator algebras. In particular, we show that two essentially free semigroup actions on totally disconnected compact spaces are continuously orbit equivalent if and only if there is a canonical abelian subalgebra preserving C*-isomorphism between the associated transformation groupoid C*-algebras. We also give some examples of orbit equivalence, consider the special case of semigroup actions by homeomorphisms and relate continuous orbit equivalence of semigroup actions to that of the associated group actions.
期刊介绍:
Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.