Hopf cyclic cohomology in braided monoidal categories

Details Hopf cyclic cohomology in braided monoidal categories Hopf cyclic cohomology in braided monoidal categories

2008-07-24

arxiv.org/abs/0807.3890v2

Mathematics

Quantum Algebra

50 pages. One reference added. Proofs are visualized through braiding diagrams. Final version to appear in `Homology, Homotopy

Scientific paper

We extend the formalism of Hopf cyclic cohomology to the context of braided categories. For a Hopf algebra in a braided monoidal abelian category we introduce the notion of stable anti-Yetter-Drinfeld module. We associate a para-cocyclic and a cocyclic object to a braided Hopf algebra endowed with a braided modular pair in involution in the sense of Connes and Moscovici. When the braiding is symmetric the full formalism of Hopf cyclic cohomology with coefficients can be extended to our categorical setting.

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