Noncommutative analogues of n-dimensional balls are defined by repeated application of the quantum double suspension to the classical low-dimensional spaces. In the ‘even-dimensional’ case they correspond to the twisted canonical commutation relations of Pusz and Woronowicz. Then quantum spheres are constructed as double manifolds of noncommutative balls. Both C*-algebras and polynomial algebras of the objects in question are defined and analysed, and their relations with previously known examples are presented. Our construction generalizes that of Hajac, Matthes, and Szymaski for ‘dimension 2’, and leads to a new class of quantum spheres (already on the C*-algebra level) in all ‘even dimensions’.
Journal of the London Mathematical Society-Second Series Vol. 77, Issue 3, p. 607-626