SPLITTINGS FOR C∗-CORRESPONDENCES AND STRONG SHIFT EQUIVALENCE
Publication Name
Mathematica Scandinavica
Abstract
We present an extension of the notion of in-splits from symbolic dynamics to topological graphs and, more generally, to C∗-correspondences. We demonstrate that in-splits provide examples of strong shift equivalences of C∗-correspondences. Furthermore, we provide a streamlined treatment of Muhly, Pask, and Tomforde’s proof that any strong shift equivalence of regular C∗correspondences induces a (gauge-equivariant) Morita equivalence between Cuntz-Pimsner algebras. For topological graphs, we prove that in-splits induce diagonal-preserving gauge-equivariant ∗-isomorphisms in analogy with the results for Cuntz-Krieger algebras. Additionally, we examine the notion of out-splits for C∗-correspondences.
Open Access Status
This publication is not available as open access
Volume
130
Issue
1
First Page
101
Last Page
148