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Home > Research literature > Preprints > Dynamical systems of type (m,n) and their C*algebras 
Imprint:  Centre de Recerca Matemàtica 2011 
Description:  38 p. 
Series:  Prepublicacions del Centre de Recerca Matemàtica ; 1050 
Abstract:  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 crossedproduct 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 crossedproduct, denoted Or m;n, is shown to be exact and nonnuclear. 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. 
Rights:  L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: 
Language:  Anglès. 
Document:  preprint 
Subject:  Sistemes dinàmics diferenciables ; Grups lliures ; C*àlgebres 
38 p, 488.4 KB 
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