Realization of a simple higher‐dimensional noncommutative torus as a transformation group C*‐algebra

Let θ be a nondegenerate skew symmetric real d × d matrix, and let A θ be the corresponding simple higher‐dimensional noncommutative torus. Suppose that d is odd, or that d ⩾4 and the entries of θ are not contained in a quadratic extension of ℚ. Then A θ 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.