Homology, Homotopy and Applications

Volume 12 (2010)

Number 1

Hopf cyclic cohomology in braided monoidal categories

Pages: 111 – 155

DOI: https://dx.doi.org/10.4310/HHA.2010.v12.n1.a9

Authors

Masoud Khalkhali (Department of Mathematics, University of Western Ontario, London, Ontario, Canada)

Arash Pourkia (Department of Mathematics, University of Western Ontario, London, Ontario, Canada)

Abstract

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.

Keywords

noncommutative geometry, Hopf algebra, braided monoidal category, Hopf cyclic cohomology

2010 Mathematics Subject Classification

58B34

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Published 1 January 2010