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Yetter-Drinfeld modules over weak Hopf algebras and the center construction

S. Caenepeel·Dingguo Wang·Yanmin Yin
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Abstract

We introduce Yetter-Drinfeld modules over a weak Hopf algebra $H$, and show that the category of Yetter-Drinfeld modules is isomorphic to the center of the category of $H$-modules. The categories of left-left, left-right, right-left and right-right Yetter-Drinfeld modules are isomorphic as braided monoidal categories. Yetter-Drinfeld modules can be viewed as weak Doi-Hopf modules, and, a fortiori, as weak entwined modules. If $H$ is finitely generated and projective, then we introduce the Drinfeld double using duality results between entwining structures and smash product structures, and show that the category of Yetter-Drinfeld modules is isomorphic to the category of modules over the Drinfeld double.

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S. Caenepeel, Dingguo Wang, Yanmin Yin. 2005-04-01. Yetter-Drinfeld modules over weak Hopf algebras and the center construction. https://arxiv.org/abs/math/0409599

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