THE TENSOR PRODUCTS OF SPHERICAL NON-COMMUTATIVE TORI WITH CUNTZ ALGEBRAS

The spherical non-commutative tori Sw were defined in [2, 3]. Assume that no non-trivial matrix algebra can be factored out of the Sw, and that the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus with a matrix algebra Mk(ℂ). It is shown that the tensor product of the spherical noncommutative torus Sw with the even Cuntz algebra O₂d has a trivial bundle structure if and only if k and 2d - 1 are relatively prime, and that the tensor product of the spherical non-commutative torus Sw with the generalized Cuntz algebra O∞ has a non-trivial bundle structure when k > 1.