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Hopf bimodules and Yetter-Drinfeld modules of Hopf algebroids (2312.03595v2)
Published 6 Dec 2023 in math.QA
Abstract: We construct Hopf bimodules and Yetter-Drinfeld modules of Hopf algebroids as a generalization of the theory for Hopf algebras. More precisely, we show that the categories of Hopf bimodules and Yetter-Drinfeld modules over a Hopf algebroid are equivalent (pre-)braided monoidal categories. Moreover, we also study the duality between finitely generated projective Yetter-Drinfeld modules.