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

2012/01/05 by Kengo Matsumoto, Matsumoto, Kengo
Mathematics · #46L35 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L35

paper · pdf · doi:10.48550/arxiv.1201.1056

19 pages

arxiv created 2012/01/05 · arxiv updated 2012/01/06

Abstract

Let \cal O_\cal 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 \cal O_\cal H^A,B_κ 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]_κ are computed by using the Euclidean algorithm.

Related

• The K-theory of Cuntz-Krieger algebras for infinite matrices
• C*-algebras associated with Hilbert C*-quad modules of C*-textile dynamical systems
• A class of representations of C^*-algebra generated by q_ij-commuting isometries
• Cuntz-Krieger algebras for infinite matrices
• The Toeplitz algebra of a Hilbert bimodule