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ABSTRACT
In this paper, we will introduce the notion of basis-related Morita equivalence in the Cuntz–Krieger algebras with their canonical right finite bases
as Hilbert C*-bimodules. We will then prove that two essential nonnegative matrices A and B are strong shift equivalent if and only if the Cuntz–Krieger algebras
and
with their canonical right finite bases are basis-relatedly Morita equivalent.
Acknowledgments
The author would like to thank the referee for his/her useful advices and suggestions. Thanks to his/her advices, the author was able to get rid of the irreducibility assumption on matrices in many places. This work was supported by JSPS KAKENHI Grant Number 15K04896.
Disclosure statement
No potential conflict of interest was reported by the author.
Additional information
Funding
Japan Society for the Promotion of Science, KAKENHI [grant number 15K04896].