Cuntz-Krieger algebras associated with Hilbert $C^*$-quad modules of commuting matrices

Details Cuntz-Krieger algebras associated with Hilbert $C^*$-quad modules of commuting matrices Cuntz-Krieger algebras associated with Hilbert $C^*$-quad modules of commuting matrices

2012-01-05

arxiv.org/abs/1201.1056v1

Mathematics

Operator Algebras

19 pages

Scientific paper

Let ${\cal O}_{{\cal H}^{A,B}_\kappa}$ be the $C^*$-algebra associated with the Hilbert $C^*$-quad module arising from commuting matrices $A,B$ with entries in $\{0,1\}$. We will show that if the associated tiling space $X_{A,B}^\kappa$ is transitive, the $C^*$-algebra ${\cal O}_{{\cal H}^{A,B}_\kappa}$ is simple and purely infinite. In particulr, for two positive integers $N,M$, the $K$-groups of the simple purely infinite $C^*$-algebra ${\cal O}_{{\cal H}^{[N],[M]}_\kappa}$ are computed by using the Euclidean algorithm.

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