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An Isaac Newton Institute Workshop

Noncommutative Geometry and Cyclic Cohomology

Periodic Hopf cyclic cohomology of bicrossed product Hopf algebras

Authors: Bahram Rangipour (Ohio State University), Henri Moscovici (Ohio State University)

Abstract

We develop intrinsic tools for computing the periodic Hopf cyclic cohomology of Hopf algebras related to transverse symmetry. Besides the Hopf algebra found by Connes and the second author in their work on the local index formula for transversely hypoelliptic operators on foliations, this family includes its `Schwarzian' quotient, on which the Rankin-Cohen universal deformation formula is based, the extended Connes-Kreimer Hopf algebra related to renormalization of divergences in QFT, as well as a series of cyclic coverings of these Hopf algebras, motivated by the treatment of transverse symmetry for nonorientable foliations.

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