Author:
ARA PERE,EXEL RUY,KATSURA TAKESHI
Abstract
AbstractGiven positive integers$n$and$m$, we consider dynamical systems in which (the disjoint union of)$n$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 denoted by${\cal O}_{m,n}$, which in turn is obtained as a quotient of the well-known Leavitt C*-algebra$L_{m,n}$, a process meant to transform the generating set of partial isometries of$L_{m,n}$into a tame set. Describing${\cal O}_{m,n}$as the crossed product of the universal$(m,n)$-dynamical system by a partial action of the free group$\mathbb {F}_{m+n}$, we show that${\cal O}_{m,n}$is not exact when$n$and$m$are both greater than or equal to 2, but the corresponding reduced crossed product, denoted by${\cal O}_{m,n}^r$, is shown to be exact and non-nuclear. Still under the assumption that$m,n\geq 2$, we prove that the partial action of$\mathbb {F}_{m+n}$is topologically free and that${\cal O}_{m,n}^r$satisfies property (SP) (small projections). We also show that${\cal O}_{m,n}^r$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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Cited by
19 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献