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Title
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L-R-Smash biproducts, double biproducts and a braided category of Yetter-Drinfeld-Long bimodules
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Author
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Abstract
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| Let H be a bialgebra and D an H-bimodule algebra and H-bicomodule coalgebra. We find sufficient conditions on D for the L-R-smash product algebra and coalgebra structures on D circle times H to form a bialgebra (in this case we say that (H, D) is an L-R-admissible pair), called L-R-smash biproduct. The Radford biproduct is a particular case, and so is, up to isomorphism, a double biproduct with trivial pairing. We construct a prebraided monoidal category LR(H), whose objects are H-bimodules H-bicomodules M endowed with left-left and right-right Yetter-Drinfeld module as well as left-right and right-left Long module structures over H, with the property that, if (H, D) is an L-R-admissible pair, the D is a bialgebra in LR(H). |
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Language
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English
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Source (journal)
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The Rocky Mountain journal of mathematics. - Provo, Utah
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Publication
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Provo, Utah
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2010
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ISSN
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0035-7596
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DOI
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10.1216/RMJ-2010-40-6-2013
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Volume/pages
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40
:6
(2010)
, p. 2013-2024
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ISI
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000286638500017
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Full text (Publisher's DOI)
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