New York Journal of Mathematics
Volume 21 (2015) 1179-1245


Kengo Matsumoto

C*-algebras associated with textile dynamical systems

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Published: November 21, 2015
Keywords: C*-algebra, symbolic dynamics, subshift, K-group, tiling
Subject: Primary 46L35, 37B10; Secondary 46L55, 37B10

A C*-symbolic dynamical system (A, ρ, Σ) is a finite family {ρα}α ∈Σ of endomorphisms of a C*-algebra A with some conditions. It yields a C*-algebra Oρ 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, {Σρ}, {Ση}, κ)
which consists of two C*-symbolic dynamical systems
(A, ρ, {Σρ}) and (A, η, {Ση})
with certain commutation relations κ between their endomorphisms {ρα}α ∈ Σρ and {ηa}a ∈ Ση. C*-textile dynamical systems yield two-dimensional subshifts and C*-algebras Oκρ,η. We will study their structure of the algebras Oκρ,η and present its K-theory formulae.


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

Author information

Department of Mathematics, Joetsu University of Education, Joetsu 943-8512, Japan