Journal of Noncommutative Geometry

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Volume 13, Issue 2, 2019, pp. 473–497
DOI: 10.4171/JNCG/327

Published online: 2019-03-15

On the anti-Yetter–Drinfeld module-contramodule correspondence

Ilya Shapiro[1]

(1) University of Windsor, Canada

We study a functor from anti-Yetter–Drinfeld modules to contramodules in the case of a Hopf algebra $H$. This functor is unpacked from the general machinery of [11]. Some byproducts of this investigation are the establishment of sufficient conditions for this functor to be an equivalence, verification that the center of the opposite category of $H$-comodules is equivalent to anti-Yetter–Drinfeld modules in contrast to [8] where the question of $H$-modules was addressed, and the observation of two types of periodicities of the generalized Yetter–Drinfeld modules introduced in [7]. Finally, we give an example of a symmetric 2-contratrace on $H$-comodules that does not arise from an anti-Yetter–Drinfeld module.

Keywords: Cyclic cohomology, anti-Yetter–Drinfeld modules, contramodules

Shapiro Ilya: On the anti-Yetter–Drinfeld module-contramodule correspondence. J. Noncommut. Geom. 13 (2019), 473-497. doi: 10.4171/JNCG/327