Cuntz-Krieger Algebras Associated with Hilbert C^*-Quad Modules of Commuting Matrices
Let O_H^A,B_κ 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^κ is transitive, the C^*-algebra O_H^A,B_κ is simple and purely infinite. In particular, for two positive integers N,M, the K-groups of the simple purely infinite C^*-algebra O_H^[N],[M]_κ are computed by using the Euclidean algorithm. , number=1, journal=MATHEMATICA SCANDINAVICA, author=Matsumoto, Kengo, year=2015, month=Sep., pages=126–149