### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 093, 16 pages      arXiv:1408.5540      https://doi.org/10.3842/SIGMA.2014.093
Contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in honor of Marc A. Rieffel

### Generalized Coefficients for Hopf Cyclic Cohomology

Mohammad Hassanzadeh, Dan Kucerovsky and Bahram Rangipour
University of New Brunswick, Fredericton, Canada

Received August 19, 2013, in final form August 22, 2014; Published online September 01, 2014

Abstract
A category of coefficients for Hopf cyclic cohomology is defined. It is shown that this category has two proper subcategories of which the smallest one is the known category of stable anti Yetter-Drinfeld modules. The middle subcategory is comprised of those coefficients which satisfy a generalized SAYD condition depending on both the Hopf algebra and the (co)algebra in question. Some examples are introduced to show that these three categories are different. It is shown that all components of Hopf cyclic cohomology work well with the new coefficients we have defined.

Key words: cyclic cohomology; Hopf algebras; noncommutative geometry.

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