$C^*$-algebras associated with asymptotic equivalence relations defined by hyperbolic toral automorphisms
Operator Algebras
2020-12-07 v2 Dynamical Systems
Abstract
We study the -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 -groups of the -algebras are described in terms of the hyperbolic matrices of the automorphisms on the torus.
Keywords
Cite
@article{arxiv.1808.00660,
title = {$C^*$-algebras associated with asymptotic equivalence relations defined by hyperbolic toral automorphisms},
author = {Kengo Matsumoto},
journal= {arXiv preprint arXiv:1808.00660},
year = {2020}
}
Comments
13 pages. Sections 1 and 4 were corrected. Sections 3 and 6 were deleted