CUNTZ-KRIEGER ALGEBRAS ASSOCIATED WITH HILBERT C*-QUAD MODULES OF COMMUTING MATRICES

摘要

Let O-H kappa A,O-B 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 O-H kappa A,O-B 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 kappa[N],O-[M] are computed by using the Euclidean algorithm.