On the anti-Yetter–Drinfeld module-contramodule correspondence
Ilya ShapiroUniversity of Windsor, Canada
We study a functor from anti-Yetter–Drinfeld modules to contramodules in the case of a Hopf algebra . This functor is unpacked from the general machinery of . 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 -comodules is equivalent to anti-Yetter–Drinfeld modules in contrast to  where the question of -modules was addressed, and the observation of two types of periodicities of the generalized Yetter–Drinfeld modules introduced in . Finally, we give an example of a symmetric 2-contratrace on -comodules that does not arise from an anti-Yetter–Drinfeld module.
Cite this article
Ilya Shapiro, On the anti-Yetter–Drinfeld module-contramodule correspondence. J. Noncommut. Geom. 13 (2019), no. 2, pp. 473–497DOI 10.4171/JNCG/327