Homology, Homotopy and Applications

Hopf cyclic cohomology in braided monoidal categories

Masoud Khalkhali and Arash Pourkia

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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.

Article information

Source
Homology Homotopy Appl., Volume 12, Number 1 (2010), 111-155.

Dates
First available in Project Euclid: 28 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.hha/1296223825

Mathematical Reviews number (MathSciNet)
MR2607413

Zentralblatt MATH identifier
1209.58008

Subjects
Primary: 58B34: Noncommutative geometry (à la Connes)

Keywords
Noncommutative geometry Hopf algebra braided monoidal category Hopf cyclic cohomology

Citation

Khalkhali, Masoud; Pourkia, Arash. Hopf cyclic cohomology in braided monoidal categories. Homology Homotopy Appl. 12 (2010), no. 1, 111--155. https://projecteuclid.org/euclid.hha/1296223825


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