A C*-symbolic dynamical system (A, ρ, Σ) is a finite family {ρ_α}_{α ∈Σ} of endomorphisms of a C*-algebra A with some conditions. It yields a C*-algebra 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 (A, ρ, η, {Σ^ρ}, {Σ^η}, κ) which consists of two C*-symbolic dynamical systems (A, ρ, {Σ^ρ}) and (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 O^κ_ρ,η. We will study their structure of the algebras O^κ_ρ,η and present its K-theory formulae.

This work was supported by JSPS KAKENHI Grant Numbers 20540215, 23540237 and 15K04896.