$C^*$-algebras arising from Dyck systems of topological Markov chains
| dc.creator | Matsumoto, Kengo | |
| dc.date | 2006-07-21 | |
| dc.date.accessioned | 2026-07-07T07:20:46Z | |
| dc.date.available | 2026-07-07T07:20:46Z | |
| dc.description | Let $A$ be an $N \times N $ irreducible matrix with entries in $\{0,1\}$. We define the topological Markov Dyck shift $D_A$ to be a nonsofic subshift consisting of the $2N$ brackets $(_1,...,(_N,)_1,...,)_N$ with both standard bracket rule and Markov chain rule coming from $A$. The subshift is regarded as a subshift defined by the canonical generators $S_1^*,..., S_N^*, S_1,..., S_N $ of the Cuntz-Krieger algebra ${\Cal O}_A$. We construct an irreducible $λ$-graph system ${{\frak L}^{Ch(D_A)}}$ that presents the subshift $D_A$ so that we have an associated simple purely infinite $C^*$-algebra ${\Cal O}_{{\frak L}^{Ch(D_A)}}$. We prove that ${\Cal O}_{{\frak L}^{Ch(D_A)}}$ is a universal unique $C^*$-algebra subject to some operator relations among $2N$ generating partial isometries. Some examples are presented such that they are not stably isomorphic to any Cuntz-Krieger algebra. | |
| dc.description | 21pages | |
| dc.identifier | https://arxiv.org/abs/math/0607518 | |
| dc.identifier | http://arxiv.org/abs/math/0607518 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115064 | |
| dc.subject | Operator Algebras | |
| dc.subject | Dynamical Systems | |
| dc.subject | 46L80 | |
| dc.title | $C^*$-algebras arising from Dyck systems of topological Markov chains | |
| dc.type | text |