On Braided Lie Structures of Algebras in the Categories of Weak Hopf Bimodules
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Let H be a weak Hopf algebra. In this paper, it is proved that the monoidal category [Formula: see text] of weak Hopf bimodules studied in Wang [19] is equivalent to the monoidal category [Formula: see text] of weak Yetter–Drinfel'd modules introduced in Böhm [2]. When H has a bijective antipode, a braiding in the category [Formula: see text] is constructed by the braiding on [Formula: see text], generalizing the main result in Schauenburg [14]. Finally, the braided Lie structures of an algebra A in the category [Formula: see text] are investigated, by showing that if A is a sum of two braided commutative subalgebras, then the braided commutator ideal of A is nilpotent.
2011 ◽
Vol 332
(1)
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pp. 244-284
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2002 ◽
Vol 26
(2)
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pp. 299-311
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2019 ◽
Vol 21
(04)
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pp. 1850045
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2018 ◽
Vol 17
(07)
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pp. 1850133
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1993 ◽
Vol 113
(1)
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pp. 45-70
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