On characteristic classes of vector bundles over quantum spheres

Abstract: We study quantizations of spaces whose K-theory in the classical limit is the ring of dual numbers Z[t]/(t^2). For a compact quantum space, we give sufficient conditions that guarantee that there is a morphism from K_0 to \Z[t]/(t^2) of abelian groups that is compatible with the tensor product of bimodules. Applications include 2-dimensional and 4-dimensional quantum spheres. We discuss in detail a quantum 4-sphere coming from quantum symplectic groups, whose K-theory is generated by the Euler class of the instanton bundle. We also construct a natural determinant line bundle over the sphere. Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page