The structure of higher-dimensional noncommutative tori and metric diophantine approximation

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Abstract

We use the cut-down method and metric diophantine approximation techniques in order to prove that the set of elements Θ = (θjk)1 ≦ j < k ≦ N with the property that the noncommutative torus AΘ is an inductive limit of direct sums of 2N-1 circle algebras and the symmetrized noncommutative torus Aσ Θ is an AF-algebra is the complement of a first category set in [0,1)N(N-1)/2. As a consequence, almost all noncommutative tori are classified by their ordered K-theory.

Original languageEnglish (US)
Pages (from-to)179-219
Number of pages41
JournalJournal fur die Reine und Angewandte Mathematik
Volume492
StatePublished - 1997
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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