On the anti-Yetter–Drinfeld module-contramodule correspondence

  • Ilya Shapiro

    University of Windsor, Canada
On the anti-Yetter–Drinfeld module-contramodule correspondence cover

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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 [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 -comodules is equivalent to anti-Yetter–Drinfeld modules in contrast to [8] where the question of -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 -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. 473–497

DOI 10.4171/JNCG/327