C*-algebras arising from Dyck systems of topological Markov chains
- Autores: Kengo Matsumoto
- Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 109, Nº 1, 2011, págs. 31-54
- Idioma: inglés
- DOI: 10.7146/math.scand.a-15176
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Resumen
Let A be an N×N irreducible matrix with entries in {0,1}. We define the topological Markov Dyck shift DA 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,S1,…,SN of the Cuntz-Krieger algebra OA. We construct an irreducible λ-graph system LCh(DA) that presents the subshift DA so that we have an associated simple purely infinite C∗-algebra OLCh(DA). We prove that OLCh(DA) is a universal unique C∗-algebra subject to some operator relations among 2N generating partial isometries.
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