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http://dx.doi.org/10.7468/jksmeb.2011.18.3.261

GROUPOID ALGEBRAS ASSOCIATED WITH COVERING MAPS  

Yi, In-Hyeop (Department of Mathematics Education, Ewha Womans University)
Publication Information
The Pure and Applied Mathematics / v.18, no.3, 2011 , pp. 261-268 More about this Journal
Abstract
For a compact Hausdorff space X with its p-fold covering map ${\sigma}$, we construct its corresponding topological groupoid ${\Gamma}$, and show that there is a strong relation between the dynamical structures of (X, ${\sigma}$) and the groupoid structures of ${\Gamma}$.
Keywords
groupoid; covering map; minimal action; irreducible action; essentially free action;
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1 J. Tomiyama: The interplay between topological dynamics and theory of $C^\ast$-algebras. Lecture Note No. 2, Res. Inst. of Math. Global Analysis Research Center, Seoul National University, 1992.
2 L.G. Brown: Stable isomorphism of hereditary subalgerbas of $C^\ast$-algebras. Pacific J. Math. 71 (1977), 335-348.   DOI
3 J. Renault: A groupoid aproach to $C^\ast$-algebras. Springer Verlag, 1980.
4 J. Cuntz: A class of $C^\ast$-algebras and topological Markov chains II: reducible chains and the Ext-functor for $C^\ast$-algebras. Invent. Math. 63 (1980) 25-40.
5 J. Cuntz & W. Krieger: A class of $C^\ast$-algebras and topological Markov chains. Invent. Math. 56 (1980) 251-268.   DOI   ScienceOn
6 A. Kumjian: Preliminary algebras arising from local homeomorphisms. Math. Scand. 52 (1983) 269-278.   DOI
7 V. Deaconu: Groupoids associated with endomorphisms. Trans. Amer. Math. Soc. 347 (1995) 1779-1786.   DOI   ScienceOn
8 W.L. Paschke: K-theory for actions of the circle group on $C^\ast$-algebras. J. Operator Theory 6 (1981) 125-133