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arXiv · 1608.04859

Imprimitivity bimodules of Cuntz--Krieger algebras and strong shift equivalences of matrices

Kengo Matsumoto
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Abstract

In this paper, we will introduce a notion of basis related Morita equivalence in the Cuntz--Krieger algebras $({{\mathcal{O}}_A}, \{S_a\}_{a \in E_A})$ with the canonical right finite basis $\{S_a\}_{a \in E_A}$ as Hilbert $C^*$-bimodule, and prove that two nonnegative irreducible matrices $A$ and $B$ are elementary equivalent, that is, $A = CD, B = DC$ for some nonnegative rectangular matrices $C, D$, if and only if the Cuntz--Krieger algebras $({{\mathcal{O}}_A}, \{S_a\}_{a \in E_A})$ and $({{\mathcal{O}}_B}, \{ S_b\}_{b\in E_B})$ with the canonical right finite bases are basis relatedly elementary Morita equivalent.

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Kengo Matsumoto. 2016-08-17. Imprimitivity bimodules of Cuntz--Krieger algebras and strong shift equivalences of matrices. https://arxiv.org/abs/1608.04859

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