Generalized coefficients for Hopf cyclic cohomology.

DOI10.3842/SIGMA.2014.093zbMATH Open1325.16007arXiv1408.5540OpenAlexW2132020191MaRDI QIDQ462638

Mohammad Hassanzadeh, Bahram Rangipour, Dan Kucerovsky

Publication date: 21 October 2014

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1408.5540

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zbMATH Keywords

Hopf algebras Hopf-cyclic cohomology stable anti-Yetter-Drinfeld modules Hopf coalgebras SAYD modules

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) (K)-theory and homology; cyclic homology and cohomology (19D55) Hopf algebras and their applications (16T05) Coalgebras and comodules; corings (16T15)