Dimension groups — 2 articles found.
Actions of $({\Bbb Z}/2{\Bbb Z})\times ({\Bbb Z}/2{\Bbb Z})$ on Lattice Ordered Dimension Groups
Andrew J. Dean, Department of Mathematical Sciences, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario, Canada P7B 5E1; e-mail: ajdean@lakeheadu.ca
Sarah K. Lucky , Department of Mathematical Sciences, Lakehead University, 955 Oliver Road, Thunder Bay, Ontario, Canada P7B 5E1; e-mail: sklucky@lakeheadu.ca
Abstract/Résumé:
It is shown that if \(G\) is a lattice ordered countable group, then every action of \(({\Bbb Z}/2{\Bbb Z})\times ({\Bbb Z}/2{\Bbb Z})\) on \(G\) arises as an inductive limit of actions of \(({\Bbb Z}/2{\Bbb Z})\times ({\Bbb Z}/2{\Bbb Z})\) on simplicial groups. Some parts of the argument work in greater generality, and are proved for general finite abelian groups. A template is given for proving similar results for other such groups.
On montre que si \(G\) est un groupe dénombrable treillis-ordonné, alors toute action de \(({\Bbb Z}/2{\Bbb Z})\times ({\Bbb Z}/2{\Bbb Z})\) sur \(G\) provient d’une limite inductive d’actions de \(({\Bbb Z}/2{\Bbb Z})\times ({\Bbb Z}/2{\Bbb Z})\) sur des groupes simpliciaux. Des parties de cet argument fonctionnent dans une généralité plus grande et sont prouvées pour des groupes abéliens finis en général. Un modèle est donné pour prouver des résultats similaires pour d’autres groupes de ce type.
Keywords: Dimension groups, K-theory, classification
AMS Subject Classification:
Classifications of $C^*$-algebras; factors, Noncommutative dynamical systems
46L35, 46L55
PDF(click to download): Actions of $({Z}/2{Z})$ x $({Z}/2{Z})$ on Lattice Ordered Dimension Groups
A Modification of the Effros-Handelman-Shen Theorem with $\mathbb{Z}_2$ actions
Bit Na Choi, Department of Mathematics and Statistics, University of New Hampshire, Durham, NH 03824, USA; e-mail: Bitna.Choi@unh.edu
Andrew J. Dean, Department of Mathematical Sciences, Lakehead University, Thunder Bay, ON, Canada P7B 5E1; e-mail: ajdean@lakeheadu.ca
Abstract/Résumé:
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 \(\mathbb{Z}_2\).
Keywords: Dimension groups, K-theory, classification
AMS Subject Classification:
Ordered abelian groups; Riesz groups; ordered linear spaces, $K_0$ as an ordered group; traces
06F20, 19K14
PDF(click to download): A Modification of the Effros-Handelman-Shen Theorem with ${Z}_2$ actions