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 language | English (US) |
---|---|
Pages (from-to) | 179-219 |
Number of pages | 41 |
Journal | Journal fur die Reine und Angewandte Mathematik |
Volume | 492 |
State | Published - 1997 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics