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

• Autores: Kengo Matsumoto
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 117, Nº 1, 2015, págs. 126-149
• Idioma: inglés
• DOI: 10.7146/math.scand.a-22239
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• Resumen

  • 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.