Title
L-R-Smash biproducts, double biproducts and a braided category of Yetter-Drinfeld-Long bimodules
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Provo, Utah ,
Subject
Mathematics
Source (journal)
The Rocky Mountain journal of mathematics. - Provo, Utah
Volume/pages
40(2010) :6 , p. 2013-2024
ISSN
0035-7596
ISI
000286638500017
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
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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