Purely infinite simple C*-algebras associated to integer dilation matrices
Operator Algebras
2010-03-11 v1 Dynamical Systems
Abstract
Given an n x n integer matrix A whose eigenvalues are strictly greater than 1 in absolute value, let \sigma_A be the transformation of the n-torus T^n=R^n/Z^n defined by \sigma_A(e^{2\pi ix})=e^{2\pi iAx} for x\in R^n. We study the associated crossed-product C*-algebra, which is defined using a certain transfer operator for \sigma_A, proving it to be simple and purely infinite and computing its K-theory groups.
Keywords
Cite
@article{arxiv.1003.2097,
title = {Purely infinite simple C*-algebras associated to integer dilation matrices},
author = {Ruy Exel and Astrid an Huef and Iain Raeburn},
journal= {arXiv preprint arXiv:1003.2097},
year = {2010}
}
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21 pages