Yetter-Drinfeld modules over weak bialgebras |
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Authors: | S Caenepeel Dingguo Wang Yanmin Yin |
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Institution: | (1) Present address: Faculty of Engineering, Vrije Universiteit Brussel, B-1050 Brussels, Belgium;(2) Present address: Department of Mathematics, Qufu Normal University, 273165 Qufu, Shandong, China;(3) Present address: Department of Mathematics, Shandong Institute of Architecture and Engineering, 250014 Jinan, Shandong, China |
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Abstract: | We discuss properties of Yetter-Drinfeld modules over weak bialgebras over commutative rings. The categories of left-left, left-right, right-left and right-right Yetter-Drinfeld modules over a weak Hopf algebra are isomorphic as braided monoidal categories. Yetter-Drinfeld modules can be viewed as weak Doi-Hopf modules, and, a fortiori, as weak entwined modules. IfH 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. The category of finitely generated projective Yetter-Drinfeld modules over a weak Hopf algebra has duality. |
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Keywords: | 16W30 |
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