Abstract
AbstractA one-sided shift of finite type $(\mathsf{X}_{A},\unicode[STIX]{x1D70E}_{A})$ determines on the one hand a Cuntz–Krieger algebra ${\mathcal{O}}_{A}$ with a distinguished abelian subalgebra ${\mathcal{D}}_{A}$ and a certain completely positive map $\unicode[STIX]{x1D70F}_{A}$ on ${\mathcal{O}}_{A}$. On the other hand, $(\mathsf{X}_{A},\unicode[STIX]{x1D70E}_{A})$ determines a groupoid ${\mathcal{G}}_{A}$ together with a certain homomorphism $\unicode[STIX]{x1D716}_{A}$ on ${\mathcal{G}}_{A}$. We show that each of these two sets of data completely characterizes the one-sided conjugacy class of $\mathsf{X}_{A}$. This strengthens a result of Cuntz and Krieger. We also exhibit an example of two irreducible shifts of finite type which are eventually conjugate but not conjugate. This provides a negative answer to a question of Matsumoto of whether eventual conjugacy implies conjugacy.
Publisher
Cambridge University Press (CUP)
Reference19 articles.
1. The primitive ideals of some étale groupoid C
∗ -algebras;Sims;Algebr. Represent. Theory,2016
2. Groupoids associated with endomorphisms
3. A Groupoid Approach to C*-Algebras
4. [4] Carlsen, T. M. , Ruiz, E. , Sims, A. and Tomforde, M. , ‘Reconstruction of groupoids and $C^{\ast }$ -rigidity of dynamical systems’, Preprint, 2017, arXiv:1711.01052, 44 pages.
Cited by
9 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