Cuntz-Krieger Algebras Associated with Hilbert $C^*$-Quad Modules of Commuting Matrices

  • Kengo Matsumoto

Abstract

Let $\mathscr{O}_{\mathscr{H}^{A,B}_{\kappa}}$ 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 $\mathscr{O}_{\mathscr{H}^{A,B}_{\kappa}}$ is simple and purely infinite. In particular, for two positive integers $N,M$, the $K$-groups of the simple purely infinite $C^*$-algebra $\mathscr{O}_{\mathscr{H}^{[N],[M]}_{\kappa}}$ are computed by using the Euclidean algorithm.
Published
2015-09-28
How to Cite
Matsumoto, K. (2015). Cuntz-Krieger Algebras Associated with Hilbert $C^*$-Quad Modules of Commuting Matrices. MATHEMATICA SCANDINAVICA, 117(1), 126-149. https://doi.org/10.7146/math.scand.a-22239
Section
Articles