<IMG BORDER="0" SRC="/proc/2006-134-01/S0002-9939-05-08129-3/gif-title0/img1.gif" >-algebras and the tail-equivalence relation on Bratteli diagrams期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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-algebras and the tail-equivalence relation on Bratteli diagrams

Authors:	R Exel J Renault

Institution:	Departamento de Matemática, Universidade Federal de Santa Catarina, 88010-970 Florianópolis, Brasil ; Département de Mathématiques, Université d'Orléans, France

Abstract:	We show that the -algebra associated to the tail-equivalence relation on a Bratteli diagram, according to a procedure recently introduced by the first-named author and A. Lopes, is isomorphic to the -algebra of the diagram. More generally we consider an approximately proper equivalence relation $\mathcal{R}=\bigcup_{n\in\mathbb{N} }\mathcal{R}_n$ on a compact space for which the quotient maps $\pi_n\colon X\to X/\mathcal R_n$ are local homeomorphisms. We show that the algebra associated to $\mathcal{R}$ under the above-mentioned procedure is isomorphic to the groupoid -algebra $C^*(\mathcal{R})$ .

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