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 language||English (US)|
|Number of pages||41|
|Journal||Journal fur die Reine und Angewandte Mathematik|
|State||Published - 1997|
ASJC Scopus subject areas
- Applied Mathematics