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

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

2010-03-10

arxiv.org/abs/1003.2097v1

Mathematics

Operator Algebras

21 pages

Scientific paper

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.

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