C*-Algebraic Characterization of Bounded Orbit Injection Equivalence for Minimal Free Cantor Systems
Abstract
Bounded orbit injection equivalence is an equivalence relation defined on minimal free Cantor systems which is a candidate to generalize flip Kakutani equivalence to actions of the Abelian free groups on more than one generator. This paper characterizes bounded orbit injection equivalence in terms of a mild strengthening of Rieffel-Morita equivalence of the associated C*-crossed-product algebras. Moreover, we construct an ordered group which is an invariant for bounded orbit injection equivalence, and does not agrees with the K\_0 group of the associated C*-crossed-product in general. This new invariant allows us to find sufficient conditions to strengthen bounded orbit injection equivalence to orbit equivalence and strong orbit equivalence.
Keywords
Cite
@article{arxiv.0903.1881,
title = {C*-Algebraic Characterization of Bounded Orbit Injection Equivalence for Minimal Free Cantor Systems},
author = {Frederic Latremoliere and Nicholas Ormes},
journal= {arXiv preprint arXiv:0903.1881},
year = {2012}
}
Comments
30 pages. Accepted in the Rocky Mountain Journal of Mathematics