C-algebras arising from Dyck systems of topological Markov chains

Authors

  • Kengo Matsumoto

DOI:

https://doi.org/10.7146/math.scand.a-15176

Abstract

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 S1,,SN,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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Published

2011-09-01

How to Cite

Matsumoto, K. (2011). C-algebras arising from Dyck systems of topological Markov chains. MATHEMATICA SCANDINAVICA, 109(1), 31–54. https://doi.org/10.7146/math.scand.a-15176

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Section

Articles