Given positive integers n and m, we consider dynamical systems in which n copies of a topological space is homeomorphic to m copies of that same space. The universal such system is shown to arise naturally from the study of a C*-algebra we denote by Om;n, which in turn is obtained as a quotient of the well known Leavitt C*-algebra Lm;n, a process meant to transform the generating set of partial isometries of Lm;n into a tame set. Describing Om;n as the crossed-product of the universal (m; n) -dynamical system by a partial action of the free group Fm+n, we show that Om;n is not exact when n and m are both greater than or equal to 2, but the corresponding reduced crossed-product, denoted Or m;n, is shown to be exact and non-nuclear. Still under the assumption that m; n >= 2, we prove that the partial action of Fm+n is topologically free and that Or m;n satisfies property (SP) (small projections). We also show that Or m;n admits no finite dimensional representations. The techniques developed to treat this system include several new results pertaining to the theory of Fell bundles over discrete groups.
eng
Centre de Recerca Matemàtica
2011