arXiv math/03072282003-07-16math.OA

AF-algebras and the tail-equivalence relation on Bratteli diagrams

R. Exel, J. Renault

备注：: 11 pages, no figures
发表信息：: Proc. Amer. Math. Soc., 134 (2006), 193 - 206

英文摘要：

Given a Bratteli diagram D we consider the compact topological space formed by all infinite paths on D. Two such path are said to be tail-equivalent when they "have the same tail", i.e. when they eventually coincide. This equivalence relation is approximately proper and hence one may consider the C*-algebra associated to it according to a procedure recently introduced by the first named author and A. Lopes. The main result of this work is the proof that this algebra is isomorphic to the AF-algebra associated to the given Bratteli diagram.

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