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06F20, Ordered abelian groups; Riesz groups; ordered linear spaces — 1 results found.

      
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A Modification of the Effros-Handelman-Shen Theorem with $\mathbb{Z}_2$ actions
C. R. Math. Rep. Acad. Sci. Canada Vol. 43 (3) 2021, pp. 87-102
Bit Na Choi; Andrew J. Dean (Received: 2021/04/08)

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We show that a \(\mathbb{Z}_2\) action on a lattice-ordered dimension group will arise as an inductive limit of \(\mathbb{Z}_2\) actions on simplicial groups. The motivation for this study is the range of invariant problem in Elliott and Su’s classification of AF type \(\mathbb{Z}_2\) actions. We modify the proof of the Effros-Handelman-Shen theorem to include \(\mathbb{Z}_2\) actions.

Nous montrons qu’une action de \(\mathbb{Z}_2\) sur un groupe de dimension ordonné par treillis apparaît comme une limite inductive d’actions de \(\mathbb{Z}_2\) sur des groupes simpliciaux. La motivation de cette étude est le problème de la gamme de l’invariant dans la classification d’Elliott et de Su des actions de \(\mathbb{Z}_2\) de type AF. Nous modifions la preuve du théorème d’Effros-Handelman-Shen pour inclure les actions de \(\mathbb{Z}_2\).

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