On the braiding on a Hopf algebra in a braided category.
Schauenburg, Peter (1998)
The New York Journal of Mathematics [electronic only]
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Displaying similar documents to “Smash (co)products and skew pairings.”
On the braiding on a Hopf algebra in a braided category.
Coalgebra deformations of bialgebras by Harrison cocycles, copairings of Hopf algebras and double crosscoproducts.
Caenepeel, S., Dăscălescu, S., Militaru, G., Panaite, F. (1997)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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Bicovariant differential calculi and cross products on braided Hopf algebras
Yuri Bespalov, Bernhard Drabant (1997)
Banach Center Publications
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In a braided monoidal category C we consider Hopf bimodules and crossed modules over a braided Hopf algebra H. We show that both categories are equivalent. It is discussed that the category of Hopf bimodule bialgebras coincides up to isomorphism with the category of bialgebra projections over H. Using these results we generalize the Radford-Majid criterion and show that bialgebra cross products over the Hopf algebra H are precisely described by H-crossed module bialgebras. In specific...
Lazy 2-cocycles over monoidal Hom-Hopf algebras
Xiaofan Zhao, Xiaohui Zhang (2016)
Colloquium Mathematicae
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We introduce the notion of a lazy 2-cocycle over a monoidal Hom-Hopf algebra and determine all lazy 2-cocycles for a class of monoidal Hom-Hopf algebras. We also study the extension of lazy 2-cocycles to a Radford Hom-biproduct.
On complements and the factorization problem of Hopf algebras
Sebastian Burciu (2011)
Open Mathematics
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Two new results concerning complements in a semisimple Hopf algebra are proved. They extend some well-known results from group theory. The uniqueness of a Krull-Schmidt-Remak type decomposition is proved for semisimple completely reducible Hopf algebras.
The coribbon structures of some finite dimensional braided Hopf algebras generated by 2×2-matrix coalgebras
Michihisa Wakui (2003)
Banach Center Publications
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We determine the coribbon structures of some finite dimensional braided Hopf algebras generated by 2×2-matrix coalgebras constructed by S. Suzuki. As a consequence, we see that such a Hopf algebra has a coribbon structure if and only if it is of Kac-Paljutkin type.
On semisimple Hopf algebras of low dimension.
Natale, Sonia (2003)
AMA. Algebra Montpellier Announcements [electronic only]
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The category of partial Doi-Hopf modules and functors
Q.-G. Chen, D.-G. Wang (2013)
Rendiconti del Seminario Matematico della Università di Padova
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Deformed enveloping algebras.
Sommerhäuser, Yorck (1996)
The New York Journal of Mathematics [electronic only]
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Braided monoidal categories and Doi-Hopf modules for monoidal Hom-Hopf algebras
Shuangjian Guo, Xiaohui Zhang, Shengxiang Wang (2016)
Colloquium Mathematicae
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We continue our study of the category of Doi Hom-Hopf modules introduced in [Colloq. Math., to appear]. We find a sufficient condition for the category of Doi Hom-Hopf modules to be monoidal. We also obtain a condition for a monoidal Hom-algebra and monoidal Hom-coalgebra to be monoidal Hom-bialgebras. Moreover, we introduce morphisms between the underlying monoidal Hom-Hopf algebras, Hom-comodule algebras and Hom-module coalgebras, which give rise to functors between the category of...
Cosemisimple Hopf algebras with antipode of arbitrary finite order.
Bichon, Julien (2002)
The New York Journal of Mathematics [electronic only]
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Representations, duals and quantum doubles of monoidal categories
Majid, Shahn
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[For the entire collection see Zbl 0742.00067.]The Tanaka-Krein type equivalence between Hopf algebras and functored monoidal categories provides the heuristic strategy of this paper. The author introduces the notion of a double cross product of monoidal categories as a generalization of double cross product of Hopf algebras, and explains some of the motivation from physics (the representation theory for double quantum groups).The Hopf algebra constructions are formulated in terms of...