Purely infinite simple C*-algebras associated to integer dilation matrices

Authors

Ruy Exel, Universidade Federal de Santa Catarina
Astrid an Huef, University of Otago
Iain Raeburn, University of WollongongFollow

RIS ID

62391

Publication Details

Exel , R., Huef, A. an. & Raeburn, I. (2011). Purely infinite simple C*-algebras associated to integer dilation matrices. Indiana University Mathematics Journal, 60 (3), 1033-1058.

Abstract

Given an n×n integer matrix A whose eigenvalues are strictly greater than 1 in absolute value, let σA be the transformation of the n-torus Tn = Rn/Zn defined by σA(e2πix) = e2πiAx for x ∈ Rn. We study the associated crossed-product C∗-algebra, which is defined using a certain transfer operator for σA, proving it to be simple and purely infinite and computing its K-theory groups.