QUASI-ROTATION CSTAR-ALGEBRAS

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 member-of T2 and A member-of GL(2, Z), 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).