C^*-algebras arising from Dyck systems of topological Markov chains
Let A be an N × N irreducible matrix with entries in {0,1}. We define the topological Markov Dyck shift D_A to be a nonsofic subshift consisting of bi-infinite sequences of the 2N brackets (_1,…,(_N,)_1,…,)_N with both standard bracket rule and Markov chain rule coming from A. It is regarded as a subshift defined by the canonical generators S_1^*,…, S_N^*, S_1,…, S_N of the Cuntz-Krieger algebra O_A. We construct an irreducible λ-graph system L^Ch (D_A) that presents the subshift D_A so that we have an associated simple purely infinite C^*-algebra O_L^Ch (D_A) . We prove that O_L^Ch (D_A) is a universal unique C^*-algebra subject to some operator relations among 2N generating partial isometries., number=1, journal=MATHEMATICA SCANDINAVICA, author=Matsumoto, Kengo, year=2011, month=Sep., pages=31–54