Journal of Operator Theory

Volume 34, Issue 1, Summer 1995 pp. 57-89.

A path model for circle algebras

Authors: Valentin Deaconu
Author institution:Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-70700, Bucharest, ROMANIA Current address: Department of Mathematics, Iowa State University, Ames, IA 50011, U.S.A.

Summary: Using groupoid theory, we construct a path model for finite type embeddings of circle algebras that generalizes the path model of Ocneanu and Sunder for Bratteli diagrams. The Jones-Watatani index is computed using the maps induced on K_0-theory by the embedding and its dual. The analysis is based on imprimitivity groupoids associated to the embeddings. Taking inductive limits, we obtain generalizations of the Bunce-Deddens algebras.

Keywords: Path model, circle algebras, imprimitivity groupoid, Jones-Watatani index, K-theory.

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