Abstract
We use the cut-down method and a multi-dimensional continued fraction approximation to prove that any simple 3-torus is an inductive limit of direct sums of four circle algebras. Consequently, simple 3-tori are classified by the orderedK 0-group with distinguished order unit.
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Communicated by H. Araki
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Lin, Q. Cut-down method in the inductive limit decomposition of non-commutative tori, III: A complete answer in 3-dimension. Commun.Math. Phys. 179, 555–575 (1996). https://doi.org/10.1007/BF02100097
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DOI: https://doi.org/10.1007/BF02100097