C^*-algebras associated with textile dynamical systems

2011/06/25 by Matsumoto, Kengo · 1 citation
#46L55 (Primary) 37B10 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1106.5092

Abstract

A C^*-symbolic dynamical system (\cal A, ρ, Σ) is a finite family \ρ_α\_α∈Σ of endomorphisms of a C^*-algebra \cal A with some conditions. It yields a C^*-algebra \cal O_ρ from an associated Hilbert C^*-bimodule. In this paper, we will extend the notion of C^*-symbolic dynamical system to C^*-textile dynamical system (\cal A, ρ, η, Σ^ρ, Σ^η, κ) which consists of two C^*-symbolic dynamical systems (\cal A, ρ, Σ^ρ) and (\cal A, η, Σ^η) with certain commutation relations κ between their endomorphisms \ρ_α\_{α∈ Σ^ρ} and \η_a \_{a ∈ Σ^η}. C^*-textile dynamical systems yield two-dimensional subshifts and C^*-algebras \cal O^κ_ρ,η. We will study the structure of the algebras \cal O^κ_ρ,η and present its K-theory formulae.

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