Journal of Noncommutative Geometry
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Published online: 2018-03-23
Hopf-dihedral (co)homology and $L$-theoryAtabey Kaygun and Serkan Sütlü (1) Istanbul Technical University, Turkey
(2) Işık University, Istanbul, Turkey
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.
Keywords: Hopf $\ast$-algebras, $L$-theory, Chern character, Hopf-dihedral cohomology
Kaygun Atabey, Sütlü Serkan: Hopf-dihedral (co)homology and $L$-theory. J. Noncommut. Geom. 12 (2018), 69-106. doi: 10.4171/JNCG/271