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- W3122589827 abstract "Abstract This paper is a continuation of the paper, Matsumoto [‘Subshifts, $lambda $ -graph bisystems and $C^*$ -algebras’, J. Math. Anal. Appl. 485 (2020), 123843]. A $lambda $ -graph bisystem consists of a pair of two labeled Bratteli diagrams satisfying a certain compatibility condition on their edge labeling. For any two-sided subshift $Lambda $ , there exists a $lambda $ -graph bisystem satisfying a special property called the follower–predecessor compatibility condition. We construct an AF-algebra ${mathcal {F}}_{mathcal {L}}$ with shift automorphism $rho _{mathcal {L}}$ from a $lambda $ -graph bisystem $({mathcal {L}}^-,{mathcal {L}}^+)$ , and define a $C^*$ -algebra ${mathcal R}_{mathcal {L}}$ by the crossed product . It is a two-sided subshift analogue of asymptotic Ruelle algebras constructed from Smale spaces. If $lambda $ -graph bisystems come from two-sided subshifts, these $C^*$ -algebras are proved to be invariant under topological conjugacy of the underlying subshifts. We present a simplicity condition of the $C^*$ -algebra ${mathcal R}_{mathcal {L}}$ and the K-theory formulas of the $C^*$ -algebras ${mathcal {F}}_{mathcal {L}}$ and ${mathcal R}_{mathcal {L}}$ . The K-group for the AF-algebra ${mathcal {F}}_{mathcal {L}}$ is regarded as a two-sided extension of the dimension group of subshifts." @default.
- W3122589827 created "2021-02-01" @default.
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- W3122589827 date "2021-01-18" @default.
- W3122589827 modified "2023-09-25" @default.
- W3122589827 title "-ALGEBRAS ASSOCIATED WITH TWO-SIDED SUBSHIFTS" @default.
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- W3122589827 doi "https://doi.org/10.1017/s144678872000049x" @default.
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