The main result in this
paper is to classify the isomorphism classes of certain non-commutative 3-tori
obtained by taking the crossed product C∗-algebra of continuous functions on the
2-torus T2 by the irrational affine quasi-rotations. Each such quasi-rotation is
represented by a pair (a,A), where a ∈ T2 and A ∈GL(2,Z), and its associated
C∗-algebra is shown to be determined (up to isomorphism) by an analogue
of the rotation angle, namely its primitive eigenvalue, by its orientation
det(A) = ±1 and a certain positive integer m(A) which comes from the
K1-group of the algebra and which determines the conjugacy class of A in
GL(2,Z).
