Hopf-dihedral (co)homology and $L$-theory

Abstract

We develop an appropriate dihedral extension of the Connes–Moscovici characteristic map for Hopf \ast -algebras. We then observe that one can use this extension together with the dihedral Chern character to detect non-trivial L -theory classes of a \ast -algebra that carry a Hopf symmetry over a Hopf \ast -algebra. Using our machinery we detect a previously unknown L -class of the standard Podleś sphere.