Classification of the crossed product C(m) × θZp for certain pairs (M, θ)

DOI10.2298/FIL1002131XzbMATH Open1307.46052arXiv1002.3959MaRDI QIDQ5412665

Yifeng Xue

Publication date: 25 April 2014

Published in: Filomat (Search for Journal in Brave)

Abstract: Let $M$ be a separable compact Hausdorff space with $dimMle2$ and $hetacolonMoM$ be a homeomorphism with prime period $p$ ($pge2$). Set $M_{h}eta=xinM|heta(x)=xot=varnothing$ and $$. Suppose that $M_0$ is dense in $M$ and $$, $$. Let $M^{\prime }$ be another separable compact Hausdorff space with $dim{M}^{\prime }le2$ and $het{a}^{\prime }$ be the self--homeomorphism of $M^{\prime }$ with prime period $p$. Suppose that $$ is dense in $M^{\prime }$. Then $$ iff there is a homeomorphism $F$ from $M/heta$ onto $M^{\prime }/het{a}^{\prime }$ such that $F(M_{h}eta)=M{\text{'}}_{het{a}^{\prime }}$. Thus, if $(M,heta)$ and $(M^{\prime },het{a}^{\prime })$ are orbit equivalent, then $$.

Full work available at URL: https://arxiv.org/abs/1002.3959

zbMATH Keywords

crossed productmatrix bundleBusby invariant

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55)

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