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

2018/08/02 by Matsumoto, Kengo
#37A55 #37D20 #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1808.00660

Abstract

We study the C^*-algebras of the étale 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 K₀-groups of the C^*-algebras are described in terms of the hyperbolic matrices of the automorphisms on the torus.

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