C*-algebras associated with Hilbert C*-quad modules of C*-textile dynamical systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:438

Article

Matsumoto, Kengo¹ 

[1] Joetsu Univ Educ, Dept Math, Joetsu 9438512, Japan

关键词: C*-algebras;    Hilbert C*-bimodules tiling;    Subshift;    Textile system;   

DOI  :  10.1016/j.jmaa.2016.02.020

来源: Elsevier

【 摘 要 】

A C*-textile dynamical system (A, rho, eta, Sigma(rho), Sigma(eta), kappa) consists of a unital C*-algebra A, two families of endomorphisms {rho alpha}alpha is an element of Sigma(rho) and {eta a}a is an element of Sigma(eta) of A and certain commutation relations kappa among them. It yields a two-dimensional subshift and a multistructure Hilbert C*-bimodule, which we call a Hilbert C*-quad module. We introduce a C*-algebra from the Hilbert C*-quad module as a two-dimensional analogue of Pimsner's construction of C*-algebras from Hilbert C*-bimodules. We study the C*-algebras defined by the Hilbert C*-quad modules and prove that they have universal properties subject to certain operator relations. We also present examples arising from commuting matrices. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free