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For pseudo-free and recurrent self-similar groups, we show that continuous orbit equivalence of inverse semigroup partial actions implies continuous orbit equivalence of group actions. Conversely, if group actions are continuous orbit equivalent, and the induced homeomorphism commutes with the shift maps on their groupoids, we obtain continuous orbit equivalence of inverse semigroup partial actions.
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참고문헌 (20)
참고문헌 신청
NATHAN BROWNLOWE / 2017 / Graph algebras and orbit equivalence / Ergodic Theory and Dynamical Systems 37(2):389~417
A. Buss / 2012 / Inverse semigroup expansions and their actions on C∗-algebras / Illinois J. Math 56(4):1185~1212
Toke Meier Carlsen / 2018 / Orbit equivalence of graphs and isomorphism of graph groupoids / MATHEMATICA SCANDINAVICA 123(2):239~248
Luiz Gustavo Cordeiro / 2020 / The dynamics of partial inverse semigroup actions / Journal of Pure and Applied Algebra 224(3):917~957
M. Dokuchaev / 2017 / Partial actions and subshifts / Journal of Functional Analysis 272(12):5038~5106
A. Buss / 2012 / Inverse semigroup expansions and their actions on C∗-algebras / Illinois J. Math 56(4):1185~1212
Toke Meier Carlsen / 2018 / Orbit equivalence of graphs and isomorphism of graph groupoids / MATHEMATICA SCANDINAVICA 123(2):239~248
Luiz Gustavo Cordeiro / 2020 / The dynamics of partial inverse semigroup actions / Journal of Pure and Applied Algebra 224(3):917~957
M. Dokuchaev / 2017 / Partial actions and subshifts / Journal of Functional Analysis 272(12):5038~5106
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