2019/06/05 by Kengo Matsumoto, Matsumoto, Kengo · 1 citation
Mathematics · Medicine · #Advanced Operator Algebra Research #Neurological disorders and treatments #Advanced Banach Space Theory
paper · pdf · doi:10.48550/arxiv.1906.01869
This paper is a continuation of the paper entitled "Subshifts, λ-graph bisystems and C^*-algebras", arXiv:1904.06464. A λ-graph bisystem consists of a pair of two labeled Bratteli diagrams satisfying certain compatibility condition on their edge labeling. For any two-sided subshift Λ, there exists a λ-graph bisystem satisfying a special property called FPCC. We will construct an AF-algebra F\frak L with shift automorphism ρ\frak L from a λ-graph bisystem (\frak L-,\frak L+), and define a C^*-algebra \mathcal R\frak L by the crossed product F\frak L\rtimes_ρ\frak Lℤ. It is a two-sided subshift analogue of asymptotic Ruelle algebras constructed from Smale spaces. If λ-graph bisystems come from two-sided subshifts, these C^*-algebras are proved to be invariant under topological conjugacy of the underlying subshifts. We will present a simplicity condition of the C^*-algebra \mathcal R\frak L and the K-theory formulas of the C^*-algebras F\frak L and \mathcal R\frak L. The K-group for the AF-algebra F\frak L is regarded as a two-sided extension of the dimension group of subshifts.