Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems

• Autorzy: S. Bezuglyi , K. Medynets
• Języki publikacji: EN

Abstrakty

EN

We consider the full group [φ] and topological full group [[φ]] of a Cantor minimal system (X,φ). We prove that the commutator subgroups D([φ]) and D([[φ]]) are simple and show that the groups D([φ]) and D([[φ]]) completely determine the class of orbit equivalence and flip conjugacy of φ, respectively. These results improve the classification found in [GPS]. As a corollary of the technique used, we establish the fact that φ can be written as a product of three involutions from [φ].

Kategorie tematyczne

• 20B99: None of the above, but in this section
• 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 110
• Numer: 2
• Strony: 409-429

Daty

wydano

2008

Twórcy

autor

S. Bezuglyi

• Institute for Low Temperature Physics, National Academy of Sciences of Ukraine, Kharkov, Ukraine

autor

K. Medynets

• Insitute for Low Temperature Physics, National Academy of Sciences of Ukraine, Kharkov, Ukraine

Identyfikatory

DOI

10.4064/cm110-2-6