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

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

2003-07-16

arxiv.org/abs/math/0307228v1

Proc. Amer. Math. Soc., 134 (2006), 193 - 206

Mathematics

Operator Algebras

11 pages, no figures

Scientific paper

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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