Itza-Ortiz, B. and Phillips, N. C., Realization of a simple higher-dimensional noncommutative torus as a transformation group C*-algebra, Bulletin of the London Mathematical Society, 40 (2008) 217226. Preprinted
Let be a nondegenerate skew symmetric real d × d matrix, and let A be the corresponding simple higher dimensional noncommutative torus. Suppose that d is odd, or that d 4 and the entries of are not contained in a quadratic extension of Q. Then A is isomorphic to the transformation group C*-algebra obtained from a minimal homeomorphism of a compact connected one dimensional space locally homeomorphic to the product of the interval and the Cantor set. The proof uses classification theory of C*-algebras.