Cuntz–Krieger algebras representations from orbits of interval maps

Let f be an expansive Markov interval map with finite transition matrix Af . Then for every point, we yield an irreducible representation of the Cuntz–Krieger algebra O Af and show that two such representations are unitarily equivalent if and only if the points belong to the same generalized orbit. The restriction of each representation to the gauge part of O Af is decomposed into irreducible representations, according to the decomposition of the orbit. © 2007 Elsevier Inc. All rights reserved.