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arXiv · 1808.00660

$C^*$-algebras associated with asymptotic equivalence relations defined by hyperbolic toral automorphisms

Kengo Matsumoto
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Abstract

We study the $C^*$-algebras of the \'etale groupoids defined by the asymptotic equivalence relations for hyperbolic automorphisms on the two-dimensional torus. The algebras are proved to be four-dimensional non-commutative tori by an explicit numerical computation. The ranges of the unique tracial states of its $K_0$-groups of the $C^*$-algebras are described in terms of the hyperbolic matrices of the automorphisms on the torus.

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Kengo Matsumoto. 2018-08-02. $C^*$-algebras associated with asymptotic equivalence relations defined by hyperbolic toral automorphisms. https://arxiv.org/abs/1808.00660

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