Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Imprimitivity bimodules of Cuntz--Krieger algebras and strong shift
  equivalences of matrices   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.

25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ