Affiliation: | a Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 4, I-34014, Trieste, Italy b Dipartimento di Scienze Matematiche, Università di Trieste, Via Valerio 12/b, I-34127, Trieste, Italy c INFN, Sezione di Napoli, Naples, Italy |
Abstract: | The quantum Euclidean spheres, SqN−1, are (noncommutative) homogeneous spaces of quantum orthogonal groups, SOq(N). The *-algebra A(SN−1q) of polynomial functions on each of these is given by generators and relations which can be expressed in terms of a self-adjoint, unipotent matrix. We explicitly construct complete sets of generators for the K-theory (by nontrivial self-adjoint idempotents and unitaries) and the K-homology (by nontrivial Fredholm modules) of the spheres SqN−1. We also construct the corresponding Chern characters in cyclic homology and cohomology and compute the pairing of K-theory with K-homology. On odd spheres (i.e., for N even) we exhibit unbounded Fredholm modules by means of a natural unbounded operator D which, while failing to have compact resolvent, has bounded commutators with all elements in the algebra A(SN−1q). |