Continuous Orbit Equivalence of Semigroup Actions  

作　　者：Xiang Qi QIANG Cheng Jun HOU 

机构地区：[1]School of Mathematical Science,Yangzhou University,Yangzhou 225002,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第6期1581-1598,共18页数学学报（英文版）

基　　金：Supported by the NSF of China(Grant No.12271469,11771379,11971419)。

摘　　要：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.

关 键 词：Semigroup action continuous one-sided orbit equivalence continuous orbit equivalence groupoid C^(∗)-algebras 

分 类 号：O152.7[理学—数学]