Free-product groups, Cuntz-Krieger algebras, and covariant maps. (English) Zbl 0769.46044
Summary: A construction is given relating a finitely generated free-product of cyclic groups with a certain Cuntz-Krieger algebra, generalizing the relation between the Choi algebra and \({\mathcal O}_ 2\). It is shown that a certain boundary action of such a group yields a Cuntz-Krieger algebra by the crossed-product construction. Certain compact convex spaces of completely positive mappings associated to a crossed-product algebra are introduced. These are used to generalize a problem of J. Anderson regarding the representation theory of the Choi algebra. An explicit computation of these spaces for the crossed-products under study yields a negative answer to this problem.
MSC:
46L55 | Noncommutative dynamical systems |
22D25 | \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations |
22D10 | Unitary representations of locally compact groups |
28D99 | Measure-theoretic ergodic theory |